Geometry and measuresGCSE / IGCSE

Rotations of shapes

Use a centre, angle and direction to rotate each vertex.

  • A complete description gives the centre, angle and direction.
  • The centre stays fixed; each vertex stays the same distance from the centre.
  • At clockwise and anticlockwise give the same result.

Example 1

Rotate triangle through anticlockwise about . Draw and label the image.

  1. Locate the centre

    Keep fixed. Keep the distance from the centre to each vertex.

  2. Turn through the angle

    Follow the curved arrow anticlockwise through . Plot each image, then join them.

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

Rotate triangle through clockwise about . Draw and label the image.

  1. Locate the centre

    Keep fixed. Keep the distance from the centre to each vertex.

  2. Turn through the angle

    Follow the curved arrow clockwise through . Plot each image, then join them.

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

Rotate triangle through anticlockwise about . 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

Rotate triangle through clockwise about . 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

Rotate triangle through anticlockwise about . 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

Rotate triangle through anticlockwise about . 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

Rotate triangle through clockwise about . 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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