Rotating shapes

The Maths Habit Handout to print

A card is pinned to a board through one corner, then turned.
Sketch where it could end up.

Many places. The pinned corner never moves, and every point stays the same distance from the pin.

Centre of rotation
The point a shape turns about.

Where does P end up?

P (3, 1) rotated 180° about (0, 0) (−3, −1)

Where does P end up?

P (0, 4) rotated 90° clockwise about (0, 0) (4, 0)

Where does P end up?

P (2, 0) rotated 90° anticlockwise about (0, 0) (0, 2)

Rotate A 90° anticlockwise about (0, 0). P′ (−3, 4)

−4−224240APBP′

Rotate A 180° about (0, 0). P′ (−3, −2)

−4−224−4−2240APBP′

Rotate A 90° anticlockwise about (0, 0). P′ (−3, 4)

−4−224240APBP′

Rotate A 90° clockwise about (1, 1). P′ (4, −2)

−112345−3−2−1123450APBP′

Rotate A 90° anticlockwise about (0, 0). P′ (−3, 4)

−4−224240APBP′

Rotate A 90° clockwise about (0, 0). P′ (1, −1)

−112345−4−3−2−112340APBP′

Rotate A 90° anticlockwise about (0, 0). P′ (−3, 4)

−4−224240APBP′

Rotate A 180° about (2, 1). P′ (0, −1)

−3−2−1123456−2−112340APBP′

Rotate A 90° anticlockwise about (0, 0). P′ (−3, 4)

−4−224240APBP′

Rotate A 90° anticlockwise about (0, −1). P′ (−2, 1)

−4−3−2−112345−2−112340APBP′

Rotating shapes worksheet, page 1

Answer sheet

  1. P (5, 2) is rotated 90° clockwise about (2, 2). Where does it end up?

    (2, −1)

  2. A shape is rotated 90° clockwise four times about the same point. Where does it end up?

    Where it started

  3. A rotation of 180° maps Q (0, 3) to Q′ (6, −1). Find the centre of rotation.

    The midpoint: (3, 1)

  1. P (4, 1) is rotated 90° clockwise about (0, 0). Write the coordinates of its image.

    (1, −4)

  2. Rotate shape A 90° anticlockwise about (2, 1). (Draw it on your ticket.)

    A123456012345

  3. A rotation of 180° maps P (−1, 4) to P′ (5, 0). Find the centre of rotation.

    (2, 2)
Exit tickets to print