Year 4: Translating points
Part of the Year 4 coordinates and translation chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Translating points
A translation is a slide. When you translate a point, you slide it to a new place. You say how many squares it moves left or right and how many it moves up or down. For example, “3 right, 2 up” means slide 3 squares to the right and then 2 squares up.
The coordinates change in a pattern. A move right or left changes the x-coordinate (the first number). A move up or down changes the y-coordinate (the second number).
| Move | What happens to the coordinates |
|---|---|
| right | x gets bigger (add) |
| left | x gets smaller (take away) |
| up | y gets bigger (add) |
| down | y gets smaller (take away) |
To describe a translation from one point to another, count how far the point goes across, and then how far up or down. The second picture shows a journey from B (1, 2) to C (6, 5).
Key ideas
- A translation slides a point left or right and up or down. It does not turn or flip.
- Say the move like this: “3 right, 2 up”. Left or right first, then up or down.
- Right: add to x. Left: take away from x. Up: add to y. Down: take away from y.
- To describe a move: compare the x-coordinates (left or right), then the y-coordinates (up or down).
- To go back, do the opposite move.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.A = (2, 3)
- Move 4 squares right. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 2 + 4 = 6
- Move 1 square up. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 3 + 1 = 4
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.A′ = (6, 4)
Check. Count on the grid from (2, 3): 4 right, 1 up gets to (6, 4). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.P = (7, 6)
- Move 3 squares left. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 7 − 3 = 4
- Move 4 squares down. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 6 − 4 = 2
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.P′ = (4, 2)
Check. Count on the grid from (7, 6): 3 left, 4 down gets to (4, 2). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.A = (1, 2) and B = (6, 5)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 1 to 6: 6 − 1 = 5
5 right - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 2 to 5: 5 − 2 = 3
3 up - Write the translation. We say the left or right move first, then the up or down move.From A to B: 5 right, 3 up
Check. Start at (1, 2) and move 5 right, 3 up: you get to (6, 5). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.C = (8, 7) and D = (3, 2)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 8 to 3: 8 − 3 = 5
5 left - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 7 to 2: 7 − 2 = 5
5 down - Write the translation. We say the left or right move first, then the up or down move.From C to D: 5 left, 5 down
Check. Start at (8, 7) and move 5 left, 5 down: you get to (3, 2). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.E = (2, 6) and F = (7, 6)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 2 to 7: 7 − 2 = 5
5 right - Compare the y-coordinates. The y-coordinate tells us how far up we are.y stays 6, so there is no move up or down.
- Write the translation. We say the left or right move first, then the up or down move.From E to F: 5 right
Check. Start at (2, 6) and move 5 right: you get to (7, 6). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Work backwards. Do the opposite of the move starting from the end point.
- Write the move and the end point. We know where the point finished.Move: 2 right, 3 up
End: (6, 5) - Undo the move. To go back to the start, do the opposite move: right becomes left, up becomes down (and the other way round).The opposite of 2 right, 3 up is 2 left, 3 down.
- Change the x-coordinate. Undo the left or right move.x: 6 − 2 = 4
- Change the y-coordinate. Undo the up or down move.y: 5 − 3 = 2
- Write the starting point. Start = (4, 2)
Check. Start at (4, 2) and move 2 right, 3 up: you reach (6, 5). ✓
Watch out. Do the opposite move. Do not do the same move again.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Do the moves one at a time. After each move write the new coordinates. Then compare the start and the end to find the one move that does the same job.
- Write the start point. We begin here.A = (1, 1)
- Do move 1: 3 right, 2 up. Change the x-coordinate for left or right. Change the y-coordinate for up or down.x: 1 + 3 = 4
y: 1 + 2 = 3
Now at (4, 3) - Do move 2: 1 left, 4 up. Change the x-coordinate for left or right. Change the y-coordinate for up or down.x: 4 − 1 = 3
y: 3 + 4 = 7
Now at (3, 7) - Find the one move that does the same job. Add up all the right and left moves (left counts as taking away). Do the same for up and down.Across: 3 + (−1) = 2
Up: 2 + 4 = 6
One move: 2 right, 6 up
Check. Start (1, 1), one move of 2 right, 6 up, end (3, 7). ✓
Watch out. Check left and right moves carefully. Left makes the x-coordinate smaller.
Watch out
Left and right change x, up and down change y. Moving a point up does not change its x-coordinate. Also say the move in the right order: (2, 3) moved 3 right and 2 up is (5, 5), not (4, 6). When going backwards, do the opposite move.Exercise 10D Translating points
Non-calculatorKey words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.P = (2, 1)
- Move 3 squares right. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 2 + 3 = 5
- Move 2 squares up. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 1 + 2 = 3
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.P′ = (5, 3)
Check. Count on the grid from (2, 1): 3 right, 2 up gets to (5, 3). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.P = (5, 4)
- Move 2 squares left. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 5 − 2 = 3
- Move 1 square up. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 4 + 1 = 5
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.P′ = (3, 5)
Check. Count on the grid from (5, 4): 2 left, 1 up gets to (3, 5). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.P = (6, 6)
- Move 4 squares left. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 6 − 4 = 2
- Move 3 squares down. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 6 − 3 = 3
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.P′ = (2, 3)
Check. Count on the grid from (6, 6): 4 left, 3 down gets to (2, 3). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.P = (1, 2)
- Move 5 squares right. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 1 + 5 = 6
- Look at the up and down move. There is no move up or down, so the y-coordinate stays the same.y stays 2
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.P′ = (6, 2)
Check. Count on the grid from (1, 2): 5 right gets to (6, 2). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.A = (1, 2) and B = (5, 4)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 1 to 5: 5 − 1 = 4
4 right - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 2 to 4: 4 − 2 = 2
2 up - Write the translation. We say the left or right move first, then the up or down move.From A to B: 4 right, 2 up
Check. Start at (1, 2) and move 4 right, 2 up: you get to (5, 4). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.B = (5, 4) and C = (7, 1)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 5 to 7: 7 − 5 = 2
2 right - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 4 to 1: 4 − 1 = 3
3 down - Write the translation. We say the left or right move first, then the up or down move.From B to C: 2 right, 3 down
Check. Start at (5, 4) and move 2 right, 3 down: you get to (7, 1). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.C = (7, 1) and D = (3, 6)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 7 to 3: 7 − 3 = 4
4 left - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 1 to 6: 6 − 1 = 5
5 up - Write the translation. We say the left or right move first, then the up or down move.From C to D: 4 left, 5 up
Check. Start at (7, 1) and move 4 left, 5 up: you get to (3, 6). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.D = (3, 6) and A = (1, 2)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 3 to 1: 3 − 1 = 2
2 left - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 6 to 2: 6 − 2 = 4
4 down - Write the translation. We say the left or right move first, then the up or down move.From D to A: 2 left, 4 down
Check. Start at (3, 6) and move 2 left, 4 down: you get to (1, 2). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.P = (3, 2)
- Move 2 squares right. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 3 + 2 = 5
- Move 4 squares up. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 2 + 4 = 6
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.P′ = (5, 6)
Check. Count on the grid from (3, 2): 2 right, 4 up gets to (5, 6). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.P = (5, 5)
- Move 3 squares left. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 5 − 3 = 2
- Move 2 squares down. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 5 − 2 = 3
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.P′ = (2, 3)
Check. Count on the grid from (5, 5): 3 left, 2 down gets to (2, 3). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.S = (4, 1) and E = (7, 5)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 4 to 7: 7 − 4 = 3
3 right - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 1 to 5: 5 − 1 = 4
4 up - Write the translation. We say the left or right move first, then the up or down move.From S to E: 3 right, 4 up
Check. Start at (4, 1) and move 3 right, 4 up: you get to (7, 5). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Work backwards. Do the opposite of the move starting from the end point.
- Write the move and the end point. We know where the point finished.Move: 3 right, 2 up
End: (7, 4) - Undo the move. To go back to the start, do the opposite move: right becomes left, up becomes down (and the other way round).The opposite of 3 right, 2 up is 3 left, 2 down.
- Change the x-coordinate. Undo the left or right move.x: 7 − 3 = 4
- Change the y-coordinate. Undo the up or down move.y: 4 − 2 = 2
- Write the starting point. Start = (4, 2)
Check. Start at (4, 2) and move 3 right, 2 up: you reach (7, 4). ✓
Watch out. Do the opposite move. Do not do the same move again.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.F = (2, 2)
- Move 3 squares right. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 2 + 3 = 5
- Look at the up and down move. There is no move up or down, so the y-coordinate stays the same.y stays 2
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.F′ = (5, 2)
Check. Count on the grid from (2, 2): 3 right gets to (5, 2). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.F = (5, 2)
- Look at the left and right move. There is no move left or right, so the x-coordinate stays the same.x stays 5
- Move 4 squares up. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 2 + 4 = 6
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.F′ = (5, 6)
Check. Count on the grid from (5, 2): 4 up gets to (5, 6). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Leo has moved the point 3 right and 2 up. Work it out carefully and compare.
- Move the x-coordinate. Moving right changes the first number. 3 right means add 3 to x.x: 2 + 3 = 5
- Move the y-coordinate. Moving up changes the second number. 2 up means add 2 to y.y: 3 + 2 = 5
- Write the right answer. The new point is (5, 5).New point = (5, 5)
- Find Leo’s mistake. Leo wrote (4, 6).He added 2 to x and 3 to y. He mixed up which move changes which number.
Check. From (2, 3) count 3 right and 2 up on the grid: you reach (5, 5). ✓
Watch out. Right and left change x. Up and down change y.
A: 4 right, 2 down B: 2 right, 4 down C: 4 left, 2 up
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Work out the move from P to Q, then find the matching box.
- Write the points. P is the start and Q is the end.P = (2, 5) and Q = (6, 3)
- Find the move. Compare the x-coordinates, then the y-coordinates.x: 2 to 6 is 4 right.
y: 5 to 3 is 2 down.
The move is 4 right, 2 down. - Match the move to a box. Look at the three boxes.Box A says “4 right, 2 down”.
Check. Start at (2, 5), 4 right and 2 down is (6, 3). ✓
Watch out. Check both numbers. Box B has the numbers the wrong way round.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Find the move that takes A to B. Then do the same move to C.
- Find the move from A to B. Compare the x-coordinates, then the y-coordinates.A (1, 1) to B (4, 3): x goes 1 to 4 = 3 right; y goes 1 to 3 = 2 up.
The move is 3 right, 2 up. - Do the same move to C (2, 5). The same move means add 3 to x and add 2 to y.x: 2 + 3 = 5
y: 5 + 2 = 7 - Write the new point. C′ = (5, 7)
Check. C moved 3 right and 2 up, the same as A to B. ✓
Watch out. Use the same move: do not use the end point of A to B.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Do the moves one at a time. After each move write the new coordinates. Then compare the start and the end to find the one move that does the same job.
- Write the start point. We begin here.P = (1, 2)
- Do move 1: 4 right, 1 up. Change the x-coordinate for left or right. Change the y-coordinate for up or down.x: 1 + 4 = 5
y: 2 + 1 = 3
Now at (5, 3) - Do move 2: 2 right, 3 up. Change the x-coordinate for left or right. Change the y-coordinate for up or down.x: 5 + 2 = 7
y: 3 + 3 = 6
Now at (7, 6) - Find the one move that does the same job. Add up all the right and left moves (left counts as taking away). Do the same for up and down.Across: 4 + 2 = 6
Up: 1 + 3 = 4
One move: 6 right, 4 up
Check. Start (1, 2), one move of 6 right, 4 up, end (7, 6). ✓
Watch out. Check left and right moves carefully. Left makes the x-coordinate smaller.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.H = (2, 2) and F = (7, 5)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 2 to 7: 7 − 2 = 5
5 right - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 2 to 5: 5 − 2 = 3
3 up - Write the translation. We say the left or right move first, then the up or down move.From H to F: 5 right, 3 up
Check. Start at (2, 2) and move 5 right, 3 up: you get to (7, 5). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Compare the x-coordinates to find the move left or right. Compare the y-coordinates to find the move up or down.
- Write the two points. Along first, then up.F = (7, 5) and H = (2, 2)
- Compare the x-coordinates. The x-coordinate tells us how far along we are. If it gets bigger the move is to the right. If it gets smaller the move is to the left.x goes from 7 to 2: 7 − 2 = 5
5 left - Compare the y-coordinates. The y-coordinate tells us how far up we are. If it gets bigger the move is up. If it gets smaller the move is down.y goes from 5 to 2: 5 − 2 = 3
3 down - Write the translation. We say the left or right move first, then the up or down move.From F to H: 5 left, 3 down
Check. Start at (7, 5) and move 5 left, 3 down: you get to (2, 2). ✓
Watch out. Left and right come from the x-coordinates (first numbers). Up and down come from the y-coordinates (second numbers).
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Think about some examples. Is the sentence true for all of them, some of them, or none?
- Try an example. Move (3, 2) up 4.(3, 2) → (3, 6). The x-coordinate stays 3.
- Think about why. Up and down moves only change the y-coordinate.The x-coordinate does not change.
- Decide. This is always true.
Check. (7, 1) moved up 2 is (7, 3). The x-coordinate is still 7. ✓
Watch out. Try some examples to test the sentence.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Think about some examples. Is the sentence true for all of them, some of them, or none?
- Try an example. Move (3, 2) right 4.(3, 2) → (7, 2). The y-coordinate stays 2.
- Think about why. Left and right moves only change the x-coordinate.The y-coordinate does not change.
- Decide. This is never true.
Check. (1, 5) moved right 3 is (4, 5). The y-coordinate is still 5. ✓
Watch out. Try some examples to test the sentence.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Think about some examples. Is the sentence true for all of them, some of them, or none?
- Try an example that works. Move (4, 4) 2 right and 2 up.(4, 4) → (6, 6). Both numbers get bigger by 2.
- Try an example that does not work. Move (4, 4) 2 left and 2 up.(4, 4) → (2, 6). The x-coordinate gets smaller.
- Decide. It depends on the move.This is sometimes true.
Check. We found one move where both numbers get bigger and one where they do not. ✓
Watch out. Try some examples to test the sentence.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Count where the point would land. The grid only shows numbers from 0 upwards.
- Move the x-coordinate. Moving left takes away from the x-coordinate.x: 3 − 4 = −1
- Look at the grid. The x-axis starts at 0. A negative number is to the left of the y-axis, off the grid.x = −1 is not on this grid.
- Decide. Zainab is right. The point would be off the grid.
Check. Z is only 3 squares from the y-axis. Moving 4 left goes past it. ✓
Watch out. The x-coordinate cannot be smaller than 0 on this grid.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Work backwards. Do the opposite of the move starting from the end point.
- Write the move and the end point. We know where the point finished.Move: 4 right, 3 up
End: (9, 7) - Undo the move. To go back to the start, do the opposite move: right becomes left, up becomes down (and the other way round).The opposite of 4 right, 3 up is 4 left, 3 down.
- Change the x-coordinate. Undo the left or right move.x: 9 − 4 = 5
- Change the y-coordinate. Undo the up or down move.y: 7 − 3 = 4
- Write the starting point. Start = (5, 4)
Check. Start at (5, 4) and move 4 right, 3 up: you reach (9, 7). ✓
Watch out. Do the opposite move. Do not do the same move again.
Key words. A translation is a slide. Every point moves the same distance in the same direction. The shape is not turned and not flipped. We describe it with left or right, and up or down.
Method. Left and right moves change the x-coordinate (the first number). Up and down moves change the y-coordinate (the second number).
- Write the starting point. Along first, then up.Q = (9, 7)
- Move 5 squares left. Moving right adds to the x-coordinate. Moving left takes away from the x-coordinate. The y-coordinate does not change here.x: 9 − 5 = 4
- Move 2 squares down. Moving up adds to the y-coordinate. Moving down takes away from the y-coordinate. The x-coordinate does not change here.y: 7 − 2 = 5
- Write the new point. Put the new x-coordinate first and the new y-coordinate second. We write a small dash after the letter for the new point.Q′ = (4, 5)
Check. Count on the grid from (9, 7): 5 left, 2 down gets to (4, 5). ✓
Watch out. Left and right change the first number. Up and down change the second number. Do not mix them up.