Describing rotations

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  1. P (2, 3) is rotated 90° clockwise about (0, 0). Write the coordinates of P′.

    (3, −2)

  2. P (−4, 1) is rotated 180° about (0, 0). Write the coordinates of P′.

    (4, −1)

  3. P (1, 5) is rotated 90° anticlockwise about (1, 2). Write the coordinates of P′.

    (−2, 2)

How could shape A have moved to land on B?
Find more than one way.

Half a turn about the point between them, or two flips at right angles.

Rotation

Angle and direction

Centre

How big is the turn?

−4−224−4−2240AB 180°

Clockwise or anticlockwise?

−4−224240AB Anticlockwise

  1. P (3, 1) goes to P′ (−3, −1) by a rotation about (0, 0). What is the angle?

    180°

  2. P (2, 0) goes to P′ (0, −2) by a rotation about (0, 0). Describe the turn.

    90° clockwise

  3. P (0, 3) goes to P′ (−3, 0) by a rotation about (0, 0). Describe the turn.

    90° anticlockwise

  4. Which three things describe a rotation fully?

    Angle, direction, centre

Describe fully the transformation from A to B. 90° anticlockwise about (0, 0)

−4−224240AB

Describe fully the transformation from A to B. 180° about (0, 0)

−4−224−4−2240AB

Describe fully the transformation from A to B. 90° anticlockwise about (0, 0)

−4−224240AB

Describe fully the transformation from A to B. 90° clockwise about (1, 1)

−112345−3−2−1123450AB

Describe fully the transformation from A to B. 90° anticlockwise about (0, 0)

−4−224240AB

Describe fully the transformation from A to B. 90° clockwise about (0, 0)

−112345−5−4−3−2−11230AB

Describe fully the transformation from A to B. 90° anticlockwise about (0, 0)

−4−224240AB

Describe fully the transformation from A to B. 180° about (1, 0)

−4−3−2−1123456−4−3−2−112340AB

Describe fully the transformation from A to B. 90° anticlockwise about (0, 0)

−4−224240AB

Describe fully the transformation from A to B. 90° anticlockwise about (−1, 1)

−5−4−3−2−1123−1123450AB

Describing rotations worksheet, page 1

Answer sheet

  1. A (1, 3) goes to A′ (3, −1)
    by a rotation about (0, 0). Describe it.

    90° clockwise

  2. Why does a rotation of 180° not need a direction?

    Both ways match

  3. A rotation of 180° maps Q (−2, 1) to Q′ (4, −3). Find the centre of rotation.

    Halfway from Q to Q′: (1, −1)

  1. A rotation about (0, 0) maps P (4, 2) to P′ (−2, 4). Describe the turn.

    90° anticlockwise

  2. Describe fully the transformation from A to B.

    Rotation 90° clockwise,
    centre (3, 4)
    AB123456701234567

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

    (2, 3)
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