Year 6: Translating on the coordinate plane
Part of the Year 6 coordinates, reflection and translation chapter. Chapter overview · whole chapter on one page
Translating on the coordinate plane
A translation slides a shape without turning or flipping it. Every corner moves the same number of squares in the same direction. To find the new coordinates, change the across number by the across move, and change the up or down number by the up or down move.
Moving right or up adds to a number. Moving left or down takes away from a number. For example, the point (-5, 3) moved 5 squares right and 4 squares down becomes (-5 + 5, 3 - 4) = (0, -1).
To describe a translation, find the change in each number. Say the across move first, then the up or down move.
Key ideas
- A translation keeps the size, the shape and the way the shape faces.
- Across change first: right adds, left takes away. Then up or down: up adds, down takes away.
- To describe a translation, say the across move first, then the up or down move.
- To undo a translation, move the image the opposite way.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of corner A.start = (-5, 3)
- Move across first. Moving 5 squares right changes the across number. Add 5.x: −5 + 5 = 0
- Move up or down. Moving 4 squares down changes the up or down number. Take away 4.y: 3 − 4 = −1
- Write the new point. Write the across number first, then the up or down number.(0, -1)
Check. Move back 5 squares left and 4 squares up and you return to (-5, 3). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Compare where the point started with where it ended, one number at a time.
- Compare the across numbers. Work out how far the across number changed.−3 to 2: 5 squares right
- Compare the up or down numbers. Work out how far the up or down number changed.−4 to −1: 3 squares up
- Write the translation. Say the across move first, then the up or down move.5 squares right and 3 squares up
Check. Start at (-3, -4) and move 5 squares right and 3 squares up: you reach (2, -1). ✓
Watch out. Say the across move first. A move with no across part is not a move to the right or left.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Undo the move: move the image the opposite way.
- Write the move. This is the move that took the point to its image.3 squares left and 4 squares down
- Undo the across move. Take the across move away from the image. This is the opposite move.x: −2 + 3 = 1
- Undo the up or down move. Take the up or down move away from the image.y: 1 + 4 = 5
- Write the original point. Write the across number first, then the up or down number.(1, 5)
Check. Move 3 squares left and 4 squares down from (1, 5) and you reach (-2, 1). ✓
Watch out. Undo a move by doing the opposite. Right becomes left, and up becomes down.
Watch out
Common mistake: moving only some of the corners. Every corner must move the same number of squares. Another mistake is to add a move to the wrong number: a move to the right changes the across number, not the up or down number.
Exercise 11C Practice: moving points and describing moves
Non-calculatorKey words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of the point.start = (2, 3)
- Move across first. Moving 4 squares right changes the across number. Add 4.x: 2 + 4 = 6
- Move up or down. Moving 1 square down changes the up or down number. Take away 1.y: 3 − 1 = 2
- Write the new point. Write the across number first, then the up or down number.(6, 2)
Check. Move back 4 squares left and 1 square up and you return to (2, 3). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of the point.start = (-3, 5)
- Move across first. Moving 6 squares right changes the across number. Add 6.x: −3 + 6 = 3
- Move up or down. Moving 2 squares down changes the up or down number. Take away 2.y: 5 − 2 = 3
- Write the new point. Write the across number first, then the up or down number.(3, 3)
Check. Move back 6 squares left and 2 squares up and you return to (-3, 5). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of the point.start = (-1, -4)
- Move across first. Moving 3 squares left changes the across number. Take away 3.x: −1 − 3 = −4
- Move up or down. Moving 5 squares up changes the up or down number. Add 5.y: −4 + 5 = 1
- Write the new point. Write the across number first, then the up or down number.(-4, 1)
Check. Move back 3 squares right and 5 squares down and you return to (-1, -4). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Compare where the point started with where it ended, one number at a time.
- Compare the across numbers. Work out how far the across number changed.−4 to 1: 5 squares right
- Compare the up or down numbers. Work out how far the up or down number changed.2 to −3: 5 squares down
- Write the translation. Say the across move first, then the up or down move.5 squares right and 5 squares down
Check. Start at (-4, 2) and move 5 squares right and 5 squares down: you reach (1, -3). ✓
Watch out. Say the across move first. A move with no across part is not a move to the right or left.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Compare where the point started with where it ended, one number at a time.
- Compare the across numbers. Work out how far the across number changed.3 to −1: 4 squares left
- Compare the up or down numbers. Work out how far the up or down number changed.−2 to 4: 6 squares up
- Write the translation. Say the across move first, then the up or down move.4 squares left and 6 squares up
Check. Start at (3, -2) and move 4 squares left and 6 squares up: you reach (-1, 4). ✓
Watch out. Say the across move first. A move with no across part is not a move to the right or left.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of the point.start = (-5, -5)
- Move across first. Moving 10 squares right changes the across number. Add 10.x: −5 + 10 = 5
- There is no move up or down. So the up or down number stays the same.y stays −5
- Write the new point. Write the across number first, then the up or down number.(5, -5)
Check. Move back 10 squares left and you return to (-5, -5). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of the origin.start = (0, 0)
- Move across first. Moving 3 squares left changes the across number. Take away 3.x: 0 − 3 = −3
- Move up or down. Moving 3 squares down changes the up or down number. Take away 3.y: 0 − 3 = −3
- Write the new point. Write the across number first, then the up or down number.(-3, -3)
Check. Move back 3 squares right and 3 squares up and you return to (0, 0). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of corner E.start = (4, -4)
- Move across first. Moving 6 squares left changes the across number. Take away 6.x: 4 − 6 = −2
- Move up or down. Moving 3 squares up changes the up or down number. Add 3.y: −4 + 3 = −1
- Write the new point. Write the across number first, then the up or down number.(-2, -1)
Check. Move back 6 squares right and 3 squares down and you return to (4, -4). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of corner W.start = (-5, -4)
- Move across first. Moving 7 squares right changes the across number. Add 7.x: −5 + 7 = 2
- Move up or down. Moving 5 squares up changes the up or down number. Add 5.y: −4 + 5 = 1
- Write the new point. Write the across number first, then the up or down number.(2, 1)
Check. Move back 7 squares left and 5 squares down and you return to (-5, -4). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of the point.start = (2, 2)
- Move across first. Moving 3 squares left changes the across number. Take away 3.x: 2 − 3 = −1
- Move up or down. Moving 3 squares down changes the up or down number. Take away 3.y: 2 − 3 = −1
- Write the new point. Write the across number first, then the up or down number.(-1, -1)
Check. Move back 3 squares right and 3 squares up and you return to (2, 2). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Do the moves one at a time, in the order they are given.
- Start with the point. Write its coordinates before any move.(0, 0)
- Move 1: translate 4 squares right and 2 squares down. Every corner moves the same number of squares, so both numbers change by the move.(0, 0) to (4, -2)
x: 0 + 4 = 4; y: 0 − 2 = −2 - Move 2: translate 6 squares left and 1 square up. Every corner moves the same number of squares, so both numbers change by the move.(4, -2) to (-2, -1)
x: 4 − 6 = −2; y: −2 + 1 = −1 - Write the final point. Write across first, then up or down.(-2, -1)
Check. Each move was checked with the number that changed. The final point is (-2, -1). ✓
Watch out. Do the moves in the order they are given. Reflecting and then translating can give a different answer from translating and then reflecting.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Compare where the point started with where it ended, one number at a time.
- Compare the across numbers. Work out how far the across number changed.−6 to 0: 6 squares right
- Compare the up or down numbers. The up or down number is the same, so there is no move up or down.4 to 4: no move
- Write the translation. Say the across move first, then the up or down move.6 squares right
Check. Start at (-6, 4) and move 6 squares right: you reach (0, 4). ✓
Watch out. Say the across move first. A move with no across part is not a move to the right or left.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of corner.start = (-2, 1)
- Move across first. Moving 5 squares right changes the across number. Add 5.x: −2 + 5 = 3
- Move up or down. Moving 3 squares down changes the up or down number. Take away 3.y: 1 − 3 = −2
- Write the new point. Write the across number first, then the up or down number.(3, -2)
Check. Move back 5 squares left and 3 squares up and you return to (-2, 1). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.
Key words. A translation slides a shape. Every point moves the same distance in the same direction. The new shape is the image. The image of corner A is written A'.
Method. Move the across number first, then the up or down number, one move at a time.
- Start at the point. Write the across number and the up or down number of corner.start = (-2, 4)
- Move across first. Moving 5 squares right changes the across number. Add 5.x: −2 + 5 = 3
- Move up or down. Moving 3 squares down changes the up or down number. Take away 3.y: 4 − 3 = 1
- Write the new point. Write the across number first, then the up or down number.(3, 1)
Check. Move back 5 squares left and 3 squares up and you return to (-2, 4). ✓
Watch out. Moving left or down takes away from the number. Moving right or up adds to it.