Grade 10 core mathematics – Rotation Quiz
1. What is a rotation in geometry?
A rotation moves every point of a figure around a fixed point (the centre) through a specified angle and direction; it does not translate, reflect or scale the figure.
2. If point (3, 1) is rotated 90° anticlockwise about the origin, what are the coordinates of its image?
Under a 90° anticlockwise rotation about the origin, (x, y) maps to (-y, x). So (3,1) → (-1,3).
3. A square is rotated by 90° about its centre. Which property remains unchanged?
A rotation is an isometry: it preserves side lengths and angles. Orientation may change visually but rotations preserve orientation (unlike reflections); the safe statement is that side lengths and angles remain unchanged.
4. Which of these is the centre of rotation property?
By definition the centre of rotation is a fixed point; all other points move on circular arcs around it.
5. If a shape is rotated 270° anticlockwise about the origin, this is equivalent to which clockwise rotation?
Rotating 270° anticlockwise equals rotating 90° clockwise because 360° - 270° = 90°.
6. Which transformation preserves orientation: rotation, reflection, or both?
Rotations preserve the orientation (clockwise order of vertices); reflections reverse orientation.
7. A rectangle (not a square) is rotated about its centre. What is the order of its rotational symmetry?
A non-square rectangle looks the same after 180° rotation and 360° rotation, so it has rotational symmetry of order 2.
8. What is the smallest positive angle of rotation that maps a regular hexagon onto itself?
A regular hexagon has 6-fold symmetry, so the smallest rotation mapping it onto itself is 360°/6 = 60°.
9. Point A is at (1, 0). After rotation about the origin it moves to (0, 1). What is the angle and direction of rotation?
(1,0) → (0,1) is a 90° turn anticlockwise about the origin.
10. A triangle is rotated through 120° about a point to match its original position. What does this say about the triangle?
Rotation by 120° (360°/3) indicates order-3 symmetry; an equilateral triangle has this property.
11. Which of the following transformations is NOT a rotation?
Sliding (translation) moves every point the same distance in the same direction and is not a rotation.
12. If a rotation matrix in the plane has determinant 1, what does this indicate about the transformation?
A 2D rotation matrix has determinant +1, indicating area is preserved and orientation is not reversed.
13. A point is 5 cm from the centre of rotation. After a rotation of 45°, what is its distance from the centre?
Rotation is an isometry: distances from the centre remain unchanged, so the distance stays 5 cm.
14. A letter 'Z' written in the same orientation is rotated 180° and still looks like a 'Z'. What is the order of rotational symmetry of the letter Z?
Since 'Z' matches itself after 180° rotation and after 360°, it has rotational symmetry of order 2.
15. Two successive rotations about the same centre are 60° and 150°. What single rotation is equivalent to these two?
Compose rotations by adding angles: 60° + 150° = 210°; equivalent to a single 210° rotation (mod 360°).
16. Which regular polygon has rotational symmetry of order 5?
A regular pentagon has 5 equal sides and 5-fold symmetry, so smallest rotation is 360°/5 and order 5.
17. A transformation maps triangle ABC to A'B'C' by a rotation. Which property must be true?
Rotations are rigid motions that preserve lengths and angles; corresponding sides and angles are equal and orientation is preserved.
18. Which angle of rotation takes point (1,1) to (-1,-1) about the origin?
A 180° rotation about the origin maps (x,y) to (-x,-y), so (1,1) → (-1,-1).
19. A star shape rotated by 72° about its centre maps onto itself. What is the order of symmetry of the star?
If rotation by 72° (360°/5) maps the figure onto itself, the shape has order-5 rotational symmetry.
20. If a point on a circle is rotated about the centre by angle θ, which of these is true?
Rotation about the centre moves points along circular arcs keeping the radial distance unchanged.
21. A regular decagon (10 sides) is rotated by 36°. Which statement is true?
360°/10 = 36°, so a regular decagon is invariant under 36° rotations and has rotational symmetry of order 10.
22. What is a rotation in geometry?
A rotation moves every point of a figure around a fixed point (the centre of rotation) through a specified angle and direction; it does not reflect, translate, or resize the figure.
23. If a point (x, y) is rotated 180° about the origin, what are the coordinates of its image?
A 180° rotation about the origin maps (x, y) to (-x, -y); both coordinates change sign and the point is diametrically opposite through the origin.
24. A triangle is rotated 90° anticlockwise about the origin. The vertex A(3, 2) maps to A'. What are the coordinates of A'?
A 90° anticlockwise rotation about the origin maps (x, y) to (-y, x); so (3, 2) becomes (-2, 3).
25. Which statement about a rotation is true?
Rotation is an isometry: it preserves lengths and angles, so the size and shape remain unchanged; it also preserves orientation (does not mirror).
26. What is the centre of rotation?
The centre of rotation is the fixed point about which every point of the figure moves through the specified angle.
27. What is the image of point (4, -1) after a 90° clockwise rotation about the origin?
A 90° clockwise rotation maps (x, y) to (y, -x) for clockwise convention; applying gives (-1, 4) when starting from (4, -1).
28. If a shape coincides with itself after a rotation of 120°, what is the order of its rotational symmetry?
Order of rotational symmetry is 360° divided by the smallest positive angle of rotation: 360° ÷ 120° = 3.
29. Which regular polygon has rotational symmetry of order 6?
A regular hexagon has 6 equal sides and angles, and 360° ÷ 6 = 60°, so it maps onto itself 6 times in a full turn (order 6).
30. A rectangle that is not a square has rotational symmetry of order:
A non-square rectangle maps onto itself after a 180° rotation and the identity (360°), giving order 2.
31. If point P is 5 cm from the centre of rotation and is rotated by 90°, how far is P' (the image) from the centre?
Rotation preserves distance from the centre, so the image remains 5 cm from the centre.
32. Which of the following transformations is a rotation of 270° anticlockwise equivalent to?
A 270° anticlockwise rotation equals a 90° clockwise rotation because 360° − 270° = 90°.
33. Under a rotation about the origin, which property of a line through the origin is preserved?
Lines through the origin are fixed as sets for rotations of 0° and 180°; other rotations map them to other lines through the origin at the rotated angle.
34. A point (2, 0) is rotated 60° anticlockwise about the origin. Which statement is correct about the distance from the origin?
Rotation preserves radial distance from the centre, so the distance from the origin stays 2.
35. Which transformation combined with a rotation can produce a reflection?
A reflection can be formed by combining rotations with reflections or other isometries; a rotation followed by reflection yields a reflection-like mapping (composition produces a glide/other isometry depending on centre and axis).
36. Which of these letters of the English alphabet has rotational symmetry of order 2 (180°) when written in capital form using standard block letters?
Capital H rotated 180° looks the same (order 2); B, N, and S do not generally map onto themselves under 180° rotation in standard block form.
37. Two successive rotations about the same centre by 40° and 100° are equivalent to a single rotation by how many degrees?
Rotations about the same centre add their angles: 40° + 100° = 140° (mod 360).
38. A regular pentagon is rotated through one step of its symmetry. What is the rotation angle?
A regular pentagon has order 5 so one step equals 360° ÷ 5 = 72°.
39. If the image of point (x, y) after a 90° anticlockwise rotation is (−y, x), what is the image after a 270° anticlockwise rotation?
A 270° anticlockwise rotation is equivalent to 90° clockwise and maps (x, y) to (y, -x).
40. Which of the following is NOT preserved under rotation?
Rotation moves points around the centre so their absolute position changes; lengths, angles and orientation are preserved.
41. A shape rotated about point O maps onto itself under 120° rotations. How many distinct positions does it occupy during a full 360° turn?
360° ÷ 120° = 3, so the shape coincides with itself three times in a full rotation (including the starting position).
42. Which matrix corresponds to a rotation of 180° about the origin in coordinate geometry? (Consider standard 2×2 rotation matrices.)
The 2×2 rotation matrix for angle θ is [[cosθ, -sinθ],[sinθ, cosθ]]. For θ = 180°, cos180° = -1 and sin180° = 0, giving [[-1,0],[0,-1]].
43. A point at (0, 3) rotates anticlockwise 90° about the origin. What is the image?
Using (x, y) → (−y, x) for 90° anticlockwise, (0, 3) maps to (−3, 0).
44. Which of the following best describes a rotation that preserves the orientation of a figure?
A rotation is a direct isometry (it preserves distances and orientation). Reflection would reverse orientation; dilation changes size.
45. If a regular equilateral triangle is rotated by 240°, this is equivalent to how many steps of 120° rotations?
Each step for an equilateral triangle is 120°; 240° = 2 × 120°, so it is equivalent to two such steps.
46. Which of the following figures has rotational symmetry of order 4?
A square maps onto itself every 90°, giving 360° ÷ 90° = 4 positions (order 4).