Question

The vertices of shape K are at (4,7), (7, 7), (7,4) and (5, 5).

The vertices of shape L are at (0, 11), (9, 11), (9, 2) and (3,5).
Shape L is an enlargement of shape K. Describe the enlargement.​

Answer 1

To find the scale factor of the enlargement, compare the distance between a pair of corresponding points from both shapes.

Shape K

A = (4, 7)

B = (7, 7)

C = (7, 4)

D = (5, 5)

Horizontal distance between A (4, 7) and B (7, 7) = 3 units

Shape L

A' = (0, 11)

B' = (9, 11)

C' = (9, 2)

D' = (3, 5)

Horizontal distance between A' (0, 11) and B' (9, 11) = 9 units

9 ÷ 3 = 3

Therefore, Shape L is an enlargement of Shape K by scale factor 3.

To find the center of dilation (enlargement), draw two lines through 2 corresponding points (e.g. A and A', B and B') - the point of intersection of these lines is the center of dilation.

Therefore, the center of enlargement is (6, 5) (refer to the second attached image).