Year 6 Maths reasoning (SATs): Translating shapes

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

1. Read the move. Every vertex moves 3 right and 1 down.
   add 3 to x and -1 to y
2. Move each vertex. Add the move to each coordinate pair.
   (0, 0) -> (3, -1) ; (2, 0) -> (5, -1) ; (2, 3) -> (5, 2) ; (0, 3) -> (3, 2)
3. Write the new coordinates. The shape has the same size and shape, only its position changes.
   (3, -1), (5, -1), (5, 2), (3, 2)
4. Write the answer.
   (3, -1), (5, -1), (5, 2), (3, 2)

Check. Each new point is 3 right and 1 down from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

1. Read the move. Every vertex moves 4 right.
   add 4 to x and 0 to y
2. Move each vertex. Add the move to each coordinate pair.
   (-3, 2) -> (1, 2) ; (-1, 2) -> (3, 2) ; (-2, 5) -> (2, 5)
3. Write the new coordinates. The shape has the same size and shape, only its position changes.
   (1, 2), (3, 2), (2, 5)
4. Write the answer.
   (1, 2), (3, 2), (2, 5)

Check. Each new point is 4 right from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

1. Read the move. Every vertex moves 5 right and 3 up.
   add 5 to x and 3 to y
2. Move each vertex. Add the move to each coordinate pair.
   (-4, -4) -> (1, -1) ; (-2, -4) -> (3, -1) ; (-4, -1) -> (1, 2)
3. Write the new coordinates. The shape has the same size and shape, only its position changes.
   (1, -1), (3, -1), (1, 2)
4. Write the answer.
   (1, -1), (3, -1), (1, 2)

Check. Each new point is 5 right and 3 up from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

1. Read the move. Every vertex moves 6 left and 4 up.
   add -6 to x and 4 to y
2. Move each vertex. Add the move to each coordinate pair.
   (1, -2) -> (-5, 2) ; (4, -2) -> (-2, 2) ; (4, -5) -> (-2, -1)
3. Write the new coordinates. The shape has the same size and shape, only its position changes.
   (-5, 2), (-2, 2), (-2, -1)
4. Write the answer.
   (-5, 2), (-2, 2), (-2, -1)

Check. Each new point is 6 left and 4 up from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

1. Read the move. Every vertex moves 3 left and 3 down.
   add -3 to x and -3 to y
2. Move each vertex. Add the move to each coordinate pair.
   (2, 1) -> (-1, -2) ; (5, 1) -> (2, -2) ; (5, 4) -> (2, 1) ; (2, 4) -> (-1, 1)
3. Write the new coordinates. The shape has the same size and shape, only its position changes.
   (-1, -2), (2, -2), (2, 1), (-1, 1)
4. Write the answer.
   (-1, -2), (2, -2), (2, 1), (-1, 1)

Check. Each new point is 3 left and 3 down from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Method. Work out the change in x and in y.

1. Change in x. 2 - (-1) = 3, so 3 right.
   +3
2. Change in y. -1 - 3 = -4, so 4 down.
   -4
3. Describe it. The move is 3 right and 4 down.
   3 right and 4 down
4. Write the answer.
   3 right and 4 down

Check. -1 + 3 = 2 and 3 - 4 = -1. ✓

Method. Test each choice against the question.

1. Read what the question asks. Decide what the answer must do or show.
2. Test the choice. (-1 + 3, 3 - 4) = (2, -1), which is 3 right and 4 down.
   3 right and 4 down fits
3. Reject the other choices. 3 left would make x smaller, and 4 up would make y bigger.
   3 left and 4 up and 3 right and 4 up do not fit
4. Write the answer.
   3 right and 4 down

Check. 3 right and 4 down is the one that fits. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. A translation slides the shape, so the size is kept and every point moves the same way.
   The shape keeps its size, Each point moves the same distance in the same direction
3. Leave the others unticked. These do not match.
   The shape is turned, The shape is flipped are not ticked
4. Write the answer.
   The shape keeps its size, Each point moves the same distance in the same direction

Check. Each ticked option is true. ✓

Watch out. A turn or a flip is not a translation.

Method. Think about what happens to each side.

1. Look at the shape. Each side moves but keeps its length.
   same lengths
2. Conclude. The shape has not changed.
   no change in size
3. Write the answer.
   No, because a translation only slides the shape, so its size and shape stay the same.

Check. Sides keep their length in a translation. ✓

Method. Subtract 4 from the x-coordinate.

1. Move left 4. Left means subtract 4 from x.
   3 - 4 = -1
2. Write the point. y stays 3.
   (-1, 3)
3. Write the answer.
   (-1, 3)

Check. (-1 + 4, 3) = (3, 3). ✓

Method. Add the move to the x-coordinate and the y-coordinate of each vertex.

1. Read the move. Every vertex moves 2 right and 2 down.
   add 2 to x and -2 to y
2. Move each vertex. Add the move to each coordinate pair.
   (-5, 0) -> (-3, -2) ; (-3, 0) -> (-1, -2) ; (-3, 2) -> (-1, 0)
3. Write the new coordinates. The shape has the same size and shape, only its position changes.
   (-3, -2), (-1, -2), (-1, 0)
4. Write the answer.
   (-3, -2), (-1, -2), (-1, 0)

Check. Each new point is 2 right and 2 down from the old one. ✓

Watch out. A translation slides the shape. Its size and shape stay the same.

Method. The bottom left corner is at (1, 1).

1. Find the move. To get from (1, 1) to (0, 0), subtract 1 from x and 1 from y.
   1 left and 1 down
2. Check the other corners. The corner (3, 1) moves to (2, 0), which keeps the shape.
   (2, 0)
3. Write the answer.
   Move it 1 left and 1 down: subtract 1 from x and from y.

Check. (1 - 1, 1 - 1) = (0, 0). ✓