Practice Maths

L63 — Rotations — Solutions

  1. Rotate 90° Clockwise

    1. (4, −1) ▶ View Solution
    2. (−2, −3) ▶ View Solution
    3. (1, 5) ▶ View Solution
    4. (6, 0) ▶ View Solution

  2. Rotate 90° Anticlockwise

    1. (−4, 1) ▶ View Solution
    2. (2, 3) ▶ View Solution
    3. (−1, −5) ▶ View Solution
    4. (−6, 0) ▶ View Solution

  3. Rotate 180°

    1. (−2, −5) ▶ View Solution
    2. (4, −3) ▶ View Solution
    3. (−1, 6) ▶ View Solution
    4. (0, 0) — origin is unchanged ▶ View Solution

  4. Rotate Shapes

    1. A(1,2) B(3,2) C(2,4) rotate 90° clockwise: A′(2,−1), B′(2,−3), C′(4,−2) ▶ View Solution
    2. P(−1,3) Q(2,3) R(0,6) rotate 90° anticlockwise: P′(−3,−1), Q′(−3,2), R′(−6,0) ▶ View Solution
    3. D(1,1) E(4,1) F(4,3) G(1,3) rotate 180°: D′(−1,−1), E′(−4,−1), F′(−4,−3), G′(−1,−3) ▶ View Solution
    4. J(2,−1) K(5,−1) L(3,−4) rotate 270° clockwise: J′(1,2), K′(1,5), L′(4,3) ▶ View Solution

  5. Comparing Rotations

    1. (4,1) rotated 90° clockwise twice: (−4, −1); single equivalent: 180° ▶ View Solution
    2. 270° clockwise vs 90° anticlockwise for (2,5): Both give (−5, 2) — they are equivalent ▶ View Solution
    3. 180° rotation about the origin ▶ View Solution
    4. 90° anticlockwise ▶ View Solution

  6. Rotation Challenges

    1. (5,0), (0,−5), (−5,0), (0,5) — returns to start ▶ View Solution
    2. Triangle A(1,0) B(3,0) C(2,2) rotated 90° anticlockwise twice: After 1st: A′(0,1), B′(0,3), C′(−2,2)  |  After 2nd: A′′(−1,0), B′′(−3,0), C′′(−2,−2) ▶ View Solution
    3. P = (5, 3) ▶ View Solution
    4. Sequence returning (4,2) to itself: Total rotation must equal 360° (e.g. 90° clockwise then 90° anticlockwise, or two 180° rotations) ▶ View Solution

  7. Mixed Rotation Drill

    1. (1,3) all rotations: 90° clockwise: (3,−1)  |  90° anticlockwise: (−3,1)  |  180°: (−1,−3)  |  270° clockwise: (−3,1) ▶ View Solution
    2. (4,−2) all rotations: 90° clockwise: (−2,−4)  |  90° anticlockwise: (2,4)  |  180°: (−4,2)  |  270° clockwise: (2,4) ▶ View Solution
    3. (−3,5) all rotations: 90° clockwise: (5,3)  |  90° anticlockwise: (−5,−3)  |  180°: (3,−5)  |  270° clockwise: (−5,−3) ▶ View Solution
    4. (0,7) all rotations: 90° clockwise: (7,0)  |  90° anticlockwise: (−7,0)  |  180°: (0,−7)  |  270° clockwise: (−7,0) ▶ View Solution

  8. Identifying the Rotation

    1. 90° anticlockwise ▶ View Solution
    2. 180° ▶ View Solution
    3. 90° clockwise ▶ View Solution
    4. 90° clockwise ▶ View Solution

  9. Rotations — Properties and Patterns

    1. Square A(1,1)B(3,1)C(3,3)D(1,3) rotated 90° clockwise: A′(1,−1), B′(1,−3), C′(3,−3), D′(3,−1); size and shape preserved ▶ View Solution
    2. (0,−5), (−5,0), (0,5), (5,0) — cycles back to start ▶ View Solution
    3. Four 90° clockwise rotations returns shape to start: True — 4 × 90° = 360°, a full turn ▶ View Solution
    4. Student A vs B — (3,4) rotated 180°: Student A is correct: (−3, −4). Student B used the y = x reflection rule instead. ▶ View Solution

  10. Rotations in Context

    1. (5, 0) ▶ View Solution
    2. (3,1) rotated 90° anticlockwise three times: 1st: (−1,3)  |  2nd: (−3,−1)  |  3rd: (1,−3) ▶ View Solution
    3. Triangle A(2,1)B(4,1)C(3,3) rotated 180° then translated right 3 up 2: After 180°: A′(−2,−1), B′(−4,−1), C′(−3,−3)  |  After translate: A′′(1,1), B′′(−1,1), C′′(0,−1) ▶ View Solution
    4. Compass rose 90° clockwise check: North → East → South → West — each is 90° clockwise; confirmed ▶ View Solution