Question

The given shape ABCD shown below has to be dilated about Vertex A by a shape factor of $\frac{3}{2}$, so the correct obtained image will be?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The given shape ABCD,Since the size is scaled by a factor of $\frac{3}{2}$, every vertex on the shape will move farther away about A.

a) Vertex A will remain the same point since the distance between Vertex A and itself is 0 m.
A1 = A = (200,100)

b) The distance of Vertex B about A is (400 - 200) = 200 m. So, B1 will move farther by
200 $\times \frac{3}{2}$ = 300 m
i.e,
B1 = (500,100)

c) The distance of Vertex C about A is (400 - 200) = 200 m along x-axis and (200 - 100) = 100 m along y-axis.
So, C1 will move farther by
200 $\times \frac{3}{2}$ = 300 along x-axis, and
100 $\times \frac{3}{2}$ = 150 m along y-axis.
i.e.,
C1 = (500,250)

d) The distance of Vertex D about A is (200 - 100) = 100 m. So, D1 will move farther by 100 $\times \frac{3}{2}$ =150 m
D1 = (200,250)

Hence, the new coordinates are: A1 = (200,100), B1 =(500,100), C1 = (500,250), D1 = (200,250).