(a) ABCDE is a pentagon. AFB, AHE and BGC are straight lines. F is the midpoint of AB. H is the midpoint of AE. G divides BC in the ratio 1: 2. AH = a, AF = a − b, BG = ED = c.

1. (a)(i)Find FH .[1]
2. (a)(ii)Using vectors, show that GD is parallel to FH.[2]
3. (a)(iii)(a)It is given that c = (4/5)a + (1/5)b. Express DC in terms of a and b.[2]
4. (a)(iii)(b)Find |AF| : |DC|.[1]
5. (b)[Figure for transformation] The transformation T maps triangle ABC onto triangle A'B'C'.
6. (b)(i)(a)Describe fully the transformation T.[2]
7. (b)(i)(b)The matrix M represents the transformation T. Find the matrix M.[2]
8. (b)(ii)Triangle A'B'C' is mapped onto triangle A"B"C" by a reflection in the y-axis. Draw and label triangle A"B"С".[1]
9. (b)(iii)Triangle ABC is mapped onto triangle A"B"C" by an anticlockwise rotation about the origin. State the angle of rotation.[1]

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