Year 4: Translating shapes
Part of the Year 4 coordinates and translation chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Translating shapes
You can translate a whole shape, not just one point. A shape is made of corners (vertices). To translate the shape, translate every corner by the same move. Then join the new corners in the same order.
A translated shape has not changed. It is the same size and the same shape. It faces the same way: it is not turned and not flipped. Only its position is different. Compare these shapes with the first triangle.
To describe how a shape has moved, choose one corner on the first shape and its matching corner on the second shape. Find the move between them. Then check that another corner makes the same move.
Key ideas
- To translate a shape, translate every corner by the same move, then join the new corners in order.
- A translation does not change the size, the shape or the way it faces. It is not turned and not flipped.
- To describe a move between two shapes, find the move from one corner to its matching corner. Check with a second corner.
- Corners of the new shape are named with a small dash: A′, B′, C′.
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. Translate every corner by the same move. Then join the new corners in the same order.
- Write the corners of the shape. We move every corner (vertex) by the same move.A = (1, 1)
B = (4, 1)
C = (1, 3) - Move every corner 3 right, 2 up. Right adds to x, left takes away from x. Up adds to y, down takes away from y.A (1, 1) → (1 + 3, 1 + 2) = A′ (4, 3)
B (4, 1) → (4 + 3, 1 + 2) = B′ (7, 3)
C (1, 3) → (1 + 3, 3 + 2) = C′ (4, 5) - Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
- Write the new coordinates. The new shape has the same size and shape as the old one.A′ (4, 3), B′ (7, 3), C′ (4, 5)
Check. Each new corner is 3 right, 2 up from the old one, and the new shape looks the same as the old shape. ✓
Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.
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. Translate every corner by the same move. Then join the new corners in the same order.
- Write the corners of the shape. We move every corner (vertex) by the same move.A = (5, 4)
B = (8, 4)
C = (8, 6)
D = (5, 6) - Move every corner 3 left, 2 down. Right adds to x, left takes away from x. Up adds to y, down takes away from y.A (5, 4) → (5 − 3, 4 − 2) = A′ (2, 2)
B (8, 4) → (8 − 3, 4 − 2) = B′ (5, 2)
C (8, 6) → (8 − 3, 6 − 2) = C′ (5, 4)
D (5, 6) → (5 − 3, 6 − 2) = D′ (2, 4) - Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
- Write the new coordinates. The new shape has the same size and shape as the old one.A′ (2, 2), B′ (5, 2), C′ (5, 4), D′ (2, 4)
Check. Each new corner is 3 left, 2 down from the old one, and the new shape looks the same as the old shape. ✓
Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.
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. Choose one corner of the first shape and find its partner corner on the second shape. Find the move between them, then check with another corner.
- Pick one corner and its partner. The corner A on the first shape matches the corner A′ on the second shape.A = (1, 2) and A′ = (5, 3)
- Find the move. Compare the x-coordinates for left or right. Compare the y-coordinates for up or down.x: 1 to 5 is 4 right.
y: 2 to 3 is 1 up. - Check with a different corner. Every corner must make the same move. If one does not, the shape has not just been translated.D (2, 4) to D′ (6, 5): 4 right, 1 up. The same move. ✓
- Write the translation. The shape moves 4 right, 1 up.
Check. Move the first shape 4 right, 1 up and it lands exactly on the second shape. ✓
Watch out. Use matching corners. Do not compare the first corner of one shape with a different corner of the other.
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. A translation slides a shape. The shape is not turned and not flipped, so it must face the same way as the first shape.
- Look at shape A. Notice which way round it faces. For example, find the corner with the right angle.
- Check each other shape. A translated shape is only slid. It is not turned and not flipped. It faces the same way as A.B: the shape is flipped over (like a mirror picture). No.
C: same way round, only moved. Yes.
D: the shape is turned round. No. - Write the answer. Only one shape has been slid without turning or flipping.The translation of A is shape C.
Check. Slide A to shape C without turning it and the two shapes match exactly. ✓
Watch out. A flipped shape looks like a mirror picture. A turned shape has been spun round. Neither is a translation.
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 from A to A′. Then move the other corners by the same move.
- Find the move. Compare the coordinates of A and A′.A (2, 3) to A′ (5, 1): x goes up 3, so 3 right; y goes down 2, so 2 down.
The move is 3 right, 2 down. - Move B and C by the same move. Add 3 to each x-coordinate and take away 2 from each y-coordinate.B (4, 3) → (4 + 3, 3 − 2) = (7, 1)
C (4, 5) → (4 + 3, 5 − 2) = (7, 3) - Check the shape. The new triangle should look the same as the old one.
Check. A′ = (5, 1), B′ = (7, 1), C′ = (7, 3). Every corner moved 3 right and 2 down. ✓
Watch out. Use the same move for every corner.
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. The perimeter is the distance all the way round.
Method. A translation does not change the size of a shape. So the sides of the new shape are the same length as the sides of the old shape.
- Find the sides of ABCD. Count squares along each side.AB goes from x = 1 to x = 5: 4 cm.
BC goes from y = 1 to y = 3: 2 cm. - Find the sides of the new shape. Count squares along each side of A′B′C′D′.A′B′ goes from x = 4 to x = 8: 4 cm.
B′C′ goes from y = 3 to y = 5: 2 cm. - Work out the perimeter of the new shape. Add all four sides.4 + 2 + 4 + 2 = 12 cm
Check. The old shape has perimeter 4 + 2 + 4 + 2 = 12 cm too. A translation does not change the perimeter. ✓
Watch out. A translation only moves the shape. It does not make it bigger or 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. Move every corner by the move, one at a time. Check that no x-coordinate or y-coordinate falls below 0.
- Move each corner 3 left. Left takes away from x.A: 2 − 3 = −1 (below 0)
B: 4 − 3 = 1
C: 2 − 3 = −1 (below 0) - Look at the grid. The grid starts at 0. A and C would be to the left of the y-axis.Two corners would be off the grid.
- Decide. The triangle cannot move 3 left on this grid.
Check. The smallest x-coordinate is 2. The shape can move at most 2 squares to the left. ✓
Watch out. Always check the corner closest to the axis.
Watch out
Move every corner, not just one. If you move only some corners the shape changes. Also remember the shape does not turn or flip: it must face the same way. And name each new corner with the same letter and a small dash, so A moves to A′.Exercise 10E Translating shapes
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. Translate every corner by the same move. Then join the new corners in the same order.
- Write the corners of the shape. We move every corner (vertex) by the same move.A = (1, 1)
B = (3, 1)
C = (1, 4) - Move every corner 4 right, 2 up. Right adds to x, left takes away from x. Up adds to y, down takes away from y.A (1, 1) → (1 + 4, 1 + 2) = A′ (5, 3)
B (3, 1) → (3 + 4, 1 + 2) = B′ (7, 3)
C (1, 4) → (1 + 4, 4 + 2) = C′ (5, 6) - Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
- Write the new coordinates. The new shape has the same size and shape as the old one.A′ (5, 3), B′ (7, 3), C′ (5, 6)
Check. Each new corner is 4 right, 2 up from the old one, and the new shape looks the same as the old shape. ✓
Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.
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. Translate every corner by the same move. Then join the new corners in the same order.
- Write the corners of the shape. We move every corner (vertex) by the same move.A = (4, 3)
B = (7, 3)
C = (7, 5)
D = (4, 5) - Move every corner 3 left, 2 down. Right adds to x, left takes away from x. Up adds to y, down takes away from y.A (4, 3) → (4 − 3, 3 − 2) = A′ (1, 1)
B (7, 3) → (7 − 3, 3 − 2) = B′ (4, 1)
C (7, 5) → (7 − 3, 5 − 2) = C′ (4, 3)
D (4, 5) → (4 − 3, 5 − 2) = D′ (1, 3) - Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
- Write the new coordinates. The new shape has the same size and shape as the old one.A′ (1, 1), B′ (4, 1), C′ (4, 3), D′ (1, 3)
Check. Each new corner is 3 left, 2 down from the old one, and the new shape looks the same as the old shape. ✓
Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.
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. Translate every corner by the same move. Then join the new corners in the same order.
- Write the corners of the shape. We move every corner (vertex) by the same move.P = (2, 2)
Q = (4, 2)
R = (4, 4)
S = (2, 4) - Move every corner 5 right. Right adds to x, left takes away from x. P (2, 2) → (2 + 5, 2 + 0) = P′ (7, 2)
Q (4, 2) → (4 + 5, 2 + 0) = Q′ (9, 2)
R (4, 4) → (4 + 5, 4 + 0) = R′ (9, 4)
S (2, 4) → (2 + 5, 4 + 0) = S′ (7, 4) - Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
- Write the new coordinates. The new shape has the same size and shape as the old one.P′ (7, 2), Q′ (9, 2), R′ (9, 4), S′ (7, 4)
Check. Each new corner is 5 right from the old one, and the new shape looks the same as the old shape. ✓
Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.
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. Translate every corner by the same move. Then join the new corners in the same order.
- Write the corners of the shape. We move every corner (vertex) by the same move.A = (1, 1)
B = (4, 1)
C = (4, 2)
D = (2, 2)
E = (2, 4)
F = (1, 4) - Move every corner 3 right, 1 up. Right adds to x, left takes away from x. Up adds to y, down takes away from y.A (1, 1) → (1 + 3, 1 + 1) = A′ (4, 2)
B (4, 1) → (4 + 3, 1 + 1) = B′ (7, 2)
C (4, 2) → (4 + 3, 2 + 1) = C′ (7, 3)
D (2, 2) → (2 + 3, 2 + 1) = D′ (5, 3)
E (2, 4) → (2 + 3, 4 + 1) = E′ (5, 5)
F (1, 4) → (1 + 3, 4 + 1) = F′ (4, 5) - Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
- Write the new coordinates. The new shape has the same size and shape as the old one.A′ (4, 2), B′ (7, 2), C′ (7, 3), D′ (5, 3), E′ (5, 5), F′ (4, 5)
Check. Each new corner is 3 right, 1 up from the old one, and the new shape looks the same as the old shape. ✓
Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.
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. Choose one corner of the first shape and find its partner corner on the second shape. Find the move between them, then check with another corner.
- Pick one corner and its partner. The corner A on the first shape matches the corner A′ on the second shape.A = (1, 1) and A′ = (5, 3)
- Find the move. Compare the x-coordinates for left or right. Compare the y-coordinates for up or down.x: 1 to 5 is 4 right.
y: 1 to 3 is 2 up. - Check with a different corner. Every corner must make the same move. If one does not, the shape has not just been translated.D (1, 3) to D′ (5, 5): 4 right, 2 up. The same move. ✓
- Write the translation. The shape moves 4 right, 2 up.
Check. Move the first shape 4 right, 2 up and it lands exactly on the second shape. ✓
Watch out. Use matching corners. Do not compare the first corner of one shape with a different corner of the other.
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. Choose one corner of the first shape and find its partner corner on the second shape. Find the move between them, then check with another corner.
- Pick one corner and its partner. The corner A on the first shape matches the corner A′ on the second shape.A = (5, 2) and A′ = (1, 4)
- Find the move. Compare the x-coordinates for left or right. Compare the y-coordinates for up or down.x: 5 to 1 is 4 left.
y: 2 to 4 is 2 up. - Check with a different corner. Every corner must make the same move. If one does not, the shape has not just been translated.C (7, 4) to C′ (3, 6): 4 left, 2 up. The same move. ✓
- Write the translation. The shape moves 4 left, 2 up.
Check. Move the first shape 4 left, 2 up and it lands exactly on the second shape. ✓
Watch out. Use matching corners. Do not compare the first corner of one shape with a different corner of the other.
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. A translation slides a shape. The shape is not turned and not flipped, so it must face the same way as the first shape.
- Look at shape A. Notice which way round it faces. For example, find the corner with the right angle.
- Check each other shape. A translated shape is only slid. It is not turned and not flipped. It faces the same way as A.B: same way round, only moved. Yes.
C: the shape is flipped over (like a mirror picture). No.
D: the shape is turned round. No. - Write the answer. Only one shape has been slid without turning or flipping.The translation of A is shape B.
Check. Slide A to shape B without turning it and the two shapes match exactly. ✓
Watch out. A flipped shape looks like a mirror picture. A turned shape has been spun round. Neither is a translation.
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. A translation moves every corner by the same move. Check what Ravi did to each corner.
- Find the move. A (1, 1) to A′ (4, 1) is 3 right. B (4, 1) to B′ (7, 1) is 3 right.The move is 3 right.
- Check corner C. C should also move 3 right: (1 + 3, 3) = (4, 3).Ravi wrote C′ = (1, 3). That is C, so he did not move it.
- Say what is wrong. Ravi forgot to move corner C. It should go to (4, 3).
Check. With C′ = (4, 3) all three corners moved 3 right. ✓
Watch out. Move every corner.
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. The move takes A to A′. Find it, then use it for the other corners.
- Find the move. Compare A and A′.A (1, 1) to A′ (3, 4): 2 right, 3 up.
- Move C by the same move. Add 2 to x and 3 to y.C (5, 3) → (5 + 2, 3 + 3) = (7, 6)
Check. C is 4 across and 2 up from A. C′ is 4 across and 2 up from A′. ✓
Watch out. Use the same move for every corner.
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. Use the same move on D.
- Remember the move. The move is 2 right and 3 up.A (1, 1) to A′ (3, 4).
- Move D. Add 2 to x and 3 to y.D (1, 3) → (1 + 2, 3 + 3) = (3, 6)
Check. D is 2 above A. D′ (3, 6) is 2 above A′ (3, 4). ✓
Watch out. Use the same move for every corner.
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 what a translation does to a shape.
- Think about what a translation does. It only slides the shape.The sides stay the same length.
- Decide. The shape cannot become bigger.This is never true.
Check. A 3 by 2 rectangle is still 3 by 2 after it slides. ✓
Watch out. A translation slides a shape. It does not change it.
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 what a translation does to a shape.
- Think about the corners. Every corner makes the same move, so the sides stay parallel and the same length.The new shape matches the old shape exactly.
- Decide. It has the same sides and the same angles.This is always true.
Check. Cut out the shape and slide it: it fits on the new shape. ✓
Watch out. A translation slides a shape. It does not change it.
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 what a translation does to a shape.
- Think about turning. When a shape turns, it faces a different way.A translation does not turn a shape.
- Decide. This is never true.
Check. A translated triangle points the same way as before. ✓
Watch out. A translation slides a shape. It does not change it.
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 what a translation does to a shape.
- Try a move that works. Move the corner (3, 3) 2 right and 1 up.(5, 4): both numbers got bigger.
- Try a move that does not work. Move the corner (3, 3) 2 left.(1, 3): the x-coordinate got smaller.
- Decide. This is sometimes true.
Check. It depends on the move. ✓
Watch out. A translation slides a shape. It does not change it.
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. The area is how many 1 cm squares fit inside.
Method. A translation does not change the size of a shape. So the new rectangle has the same length and width as the old one.
- Find the length and the width. Count squares along the sides of ABCD.Length: 6 − 2 = 4 cm. Width: 5 − 2 = 3 cm.
- Work out the perimeter. Add all four sides.4 + 3 + 4 + 3 = 14 cm
- Work out the area. Multiply the length by the width.4 × 3 = 12 cm²
Check. After a slide the shape is the same size, so the answer is the same as for ABCD. ✓
Watch out. A translation does not change the perimeter or the area.
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. Move each corner. If any coordinate is below 0, the shape is off the grid.
- Move every corner. Left takes away from x. Down takes away from y.A: (2 − 3, 1 + 0) = (-1, 1)
B: (4 − 3, 1 + 0) = (1, 1)
C: (2 − 3, 4 + 0) = (-1, 4) - Look for a number below 0. The grid starts at 0 on both axes.The corners A and C have a negative number: they are off the grid.
- Answer. No, it cannot be done on this grid.
Check. The lowest x-coordinate is 2 and the lowest y-coordinate is 1. ✓
Watch out. Check the corners closest to the axes.
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. Translate every corner by the same move. Then join the new corners in the same order.
- Write the corners of the shape. We move every corner (vertex) by the same move.A = (2, 1)
B = (4, 1)
C = (2, 4) - Move every corner 2 left. Right adds to x, left takes away from x. A (2, 1) → (2 − 2, 1 + 0) = A′ (0, 1)
B (4, 1) → (4 − 2, 1 + 0) = B′ (2, 1)
C (2, 4) → (2 − 2, 4 + 0) = C′ (0, 4) - Plot the new corners and join them in order. The new shape (orange) is the old shape (blue) after the slide. The arrows show the move.
- Write the new coordinates. The new shape has the same size and shape as the old one.A′ (0, 1), B′ (2, 1), C′ (0, 4)
Check. Each new corner is 2 left from the old one, and the new shape looks the same as the old shape. ✓
Watch out. Move every corner by the same amount. If one corner is missed, the shape gets squashed.
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. Move each corner. If any coordinate is below 0, the shape is off the grid.
- Move every corner. Left takes away from x. Down takes away from y.A: (2 + 0, 1 − 2) = (2, -1)
B: (4 + 0, 1 − 2) = (4, -1)
C: (2 + 0, 4 − 2) = (2, 2) - Look for a number below 0. The grid starts at 0 on both axes.The corners A and B have a negative number: they are off the grid.
- Answer. No, it cannot be done on this grid.
Check. The lowest x-coordinate is 2 and the lowest y-coordinate is 1. ✓
Watch out. Check the corners closest to the axes.
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 two moves one after the other. Then work out the one move that has the same effect.
- Do the first move. 3 right and 1 up: add 3 to x and add 1 to y.A (1, 1) → (4, 2)
B (3, 1) → (6, 2)
C (1, 3) → (4, 4) - Do the second move. 2 left and 4 up: take away 2 from x and add 4 to y.A (4, 2) → (2, 6)
B (6, 2) → (4, 6)
C (4, 4) → (2, 8) - Find the one move that does the same job. Add the left and right moves, and add the up and down moves.Across: 3 − 2 = 1 right
Up: 1 + 4 = 5 up
One move: 1 right, 5 up
Check. A (1, 1) → (2, 6): 1 right and 5 up. ✓
Watch out. Left takes away from x, so 3 right then 2 left is 1 right.