1. The problem is to enlarge shapes by given scale factors from specified centres of enlargement. 2. The formula for enlargement of a point $(x,y)$ from centre $(x_c,y_c)$ with scale factor $k$ is: $$ (x',y') = (x_c + k(x - x_c), y_c + k(y - y_c)) $$ This means you subtract the centre coordinates from the point, multiply by the scale factor, then add back the centre coordinates. 3. For the first shape (a) with centre $P=(1,1)$ and scale factor $2$: - Original vertices approximately: $(1,1), (2,1), (2,2)$ - Apply formula: - For $(1,1)$: $(1 + 2(1-1), 1 + 2(1-1)) = (1,1)$ (centre stays the same) - For $(2,1)$: $(1 + 2(2-1), 1 + 2(1-1)) = (1 + 2, 1) = (3,1)$ - For $(2,2)$: $(1 + 2(2-1), 1 + 2(2-1)) = (3,3)$ 4. For the second shape (b) with centre $P=(2,1)$ and scale factor $3$: - Original vertices approximately: $(2,1), (4,1), (4,2), (2,2)$ - Apply formula: - For $(2,1)$: $(2 + 3(2-2), 1 + 3(1-1)) = (2,1)$ - For $(4,1)$: $(2 + 3(4-2), 1 + 3(1-1)) = (2 + 6, 1) = (8,1)$ - For $(4,2)$: $(2 + 3(4-2), 1 + 3(2-1)) = (8,4)$ - For $(2,2)$: $(2 + 3(2-2), 1 + 3(2-1)) = (2,4)$ 5. For the third shape (a) with centre $(4,-3)$ and scale factor $2$: - Original vertices approximately: $(2,-5), (3,-5), (3,-4)$ - Apply formula: - For $(2,-5)$: $(4 + 2(2-4), -3 + 2(-5+3)) = (4 + 2(-2), -3 + 2(-2)) = (4 - 4, -3 - 4) = (0,-7)$ - For $(3,-5)$: $(4 + 2(3-4), -3 + 2(-5+3)) = (4 + 2(-1), -3 - 4) = (2,-7)$ - For $(3,-4)$: $(4 + 2(3-4), -3 + 2(-4+3)) = (2, -3 + 2(-1)) = (2,-5)$ 6. For the fourth shape (b) with centre $(3,2)$ and scale factor $3$: - Original vertices approximately: $(2,1), (3,1), (3,3)$ - Apply formula: - For $(2,1)$: $(3 + 3(2-3), 2 + 3(1-2)) = (3 + 3(-1), 2 + 3(-1)) = (0,-1)$ - For $(3,1)$: $(3 + 3(3-3), 2 + 3(1-2)) = (3, -1)$ - For $(3,3)$: $(3 + 3(3-3), 2 + 3(3-2)) = (3, 5)$ These are the enlarged coordinates for each shape using the given centres and scale factors.