Geometry and measuresKey Stage 3

Translations of shapes

Use a column vector to move every vertex.

  • The top number gives horizontal movement: positive right, negative left.
  • The bottom number gives vertical movement: positive up, negative down.
  • Shape, size and orientation are unchanged.

Example 1

Translate triangle by . Draw and label the image.

  1. Read the vector

    4 right and 2 down.

  2. Move every vertex

    Use exactly the same movement for all three vertices. Join their images in the same order.

Original shape
Original shape ABC on an equal-scale coordinate grid.
Original and image
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.
OriginalImageConstruction

Example 2

Translate triangle by . Draw and label the image.

  1. Read the vector

    3 left and 2 up.

  2. Move every vertex

    Use exactly the same movement for all three vertices. Join their images in the same order.

Original shape
Original shape ABC on an equal-scale coordinate grid.
Original and image
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.
OriginalImageConstruction

Remember
Use corresponding vertices to check the whole shape, not just one side.

Your turn

Question 1

Translate triangle by . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 2

Translate triangle by . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 3

Translate triangle by . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 4

Translate triangle by . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 5

Translate triangle by . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

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