## Rotation Exercise

1. For the equilateral triangle shown, describe the rotations that map:

 (a) A to B (b) A to C (c) B to C

2. ABCA´B´ C´  under a rotation of 90°about A

(a) Name an invariant point.

(b) Complete AB  ....................

(c) ABC  ....................

(d) What transformation would map A´B´ C´  to ABC

(e) What is the size of BCC´

3. What are the coordinates of the points shown under the given rotations:

 (a) A, under a rotation of 180°, about (0, 0) (b) C, under rotation of − 90°, about (0, 0) (c) D, under rotation of 180°, about (- 1, 0) (d) B, under rotation of 270°, about (0, 2)

4. Copy the diagrams and locate the centres of rotation that map PQR to P´Q´R´ and measure the angle of rotation.

 (a) (b)

5. (a) Rotate the rectangle ABCD about point A through an angle of rotation 180°.

Label the images A´B´C´D´.

(b) Rotate rectangle AB´C´ D´  about D´ through an angle of rotation of -45°.

Label the images A´´B´´C´´D´´.

6.

 (a) Rotate triangle XYZ through an angle of 180° about point A, (5, 5). (b) Give the co-ordinates of the vertices of the image triangle X´Y´ Z´ . (c) What is the size of angle YAY´ ? (d) XY measures 2 units. What is the length of X´Y´ ?