(a) Triangle ABC has vertices A(2, 2), B(3, 5) and C(4, 1). Triangle A'B'C' has vertices A'(−4, 4), Β΄(−3, 7) and C'(−2, 3). (b) PQRS is a parallelogram. The position vector of P relative to O is given by OP = ((-4), (2)). The position vector of Q relative to O is given by OQ = ((4), (6)). [Figure 11.1] (c) [Figure 11.2] The diagram shows triangle D.

1. (a)Write down the column vector of the translation that maps triangle ABC onto triangle A'B'C' .[1]
2. (b)(i)Express PQ as a column vector.[2]
3. (b)(ii)Find RS.[1]
4. (b)(iii)Find |RS|.[2]
5. (c)(i)An enlargement with centre (5, 4), scale factor 2, maps triangle D onto triangle E. Draw and label triangle E.[2]
6. (c)(ii)An enlargement with centre (5, 4), scale factor 0.5, maps triangle D onto triangle F. Draw and label triangle F.[1]
7. (c)(iii)Triangle G has vertices (5, 4), (4, 3) and (3, 5). Triangle F can be mapped onto triangle G using a single enlargement. Triangle F can also be mapped onto triangle G using a different single transformation T. Describe fully the single transformation T.[3]

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