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1. For the equilateral triangle shown, describe the rotations that map:
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(a) A to B
(b) A to C
(c) B to C
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2.  ABC A´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:
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(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)
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4. Copy the diagrams and locate the centres of rotation that map PQR to P´Q´R´ and measure the angle of rotation.
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(a)
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(b)
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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.
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(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´ ?
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