[Figure 7.1] In the triangle ABC, D divides AB in the ratio 3 : 2, and E divides AC in the ratio 3 : 2. AD = a and AE = b. [Figure 7.2] Triangle A has vertices (3, 1), (5, 1) and (5, 4). The transformation S₁ is represented by the matrix (2 0 / 0 1). S₁ maps triangle A onto triangle B. The transformation S₂ is represented by the matrix (1 0 / 1 1).

1. (a)(i)Show, using vectors, that DE is parallel to BC.[3]
2. (a)(ii)Find the ratio Area of triangle ADE : Area of triangle ABC.[2]
3. (b)(i)Draw and label triangle B.[2]
4. (b)(ii)What type of transformation is S₁?[1]
5. (b)(iii)Find the matrix that represents the combined transformation S₂S₁.[2]
6. (b)(iv)The combined transformation S₂S₁ maps triangle A onto triangle C. Find the matrix which represents the transformation that maps triangle C onto triangle A.[2]

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