Using a scale of 2 cm to represent 1 unit on each axis, draw x and y axes for -3 ≤ x ≤ 7 and -3 ≤ y ≤ 7.

(a) Triangle ABC has vertices A(3, 6), B(3, 7) and C(1, 7). Triangle A1B1C1 has vertices A1(-1, 4), B1(-2, 4) and C1(-2, 2).

(a(i)) Draw and label triangle ABC and triangle A1B1C1.[2]

(a(ii)) Describe fully a single transformation which maps triangle ABC onto triangle A1B1C1.[2]

(b) The matrix 0110 maps triangle ABC onto triangle A2B2C2.

(b(i)) Find the coordinates of triangle A2B2C2.[2]

(b(ii)) Draw and label triangle A2B2C2.[1]

(c) Triangle A1B1C1 can be mapped onto triangle A3B3C3 by a translation. Given that A3 is the point (3, -1),

(c(i)) find the column vector representing this translation,[1]

(c(ii)) draw and label triangle A3B3C3.[1]

(d) Triangle A4B4C4 has vertices A4(0, 3), B4(0, 1) and C4(4, 1).

(d(i)) Draw and label triangle A4B4C4.[1]

(d(ii)) Describe fully the transformation which maps triangle ABC onto triangle A4B4C4.[2]