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.