Question

If rectangle ABCD is dilated by a scale factor of 1.5 with a center of dilation at vertex A, how does the area of A'B'C'D' compare with the area of ABCD?
A) The area of A'B'C'D' is 3 times the area of ABCD.
B) The area of A'B'C'D' is 6 times the area of ABCD.
C) The area of A'B'C'D' is 1.5 times the area of ABCD.
D) The area of A'B'C'D' is 2.25 times the area of ABCD.

Answer 1

The Answer................  D

Answer 2

Answer:

D is correct.  

The area of A'B'C'D' is 2.25 times the area of ABCD.

Step-by-step explanation:

If a rectangle ABCD is dilated by a scale factor of 1.5 with a center of dilation at vertex A.

Dilated rectangle is A'B'C'D'. Center of dilation is A.

Therefore, A=A'

Scale factor is 1.5

A'B'=1.5 AB

A'D'=1.5 AD

Area of rectangle ABCD = AB x AD

Area of rectangle A'B'C'D' = A'B' x A"D"

Area of rectangle A'B'C'D' = 1.5 AB x 1.5 AD

Area of rectangle A'B'C'D' = 1.5 x 1.5 ( ABxAD)

Area of rectangle A'B'C'D' = 2.25 x Area of rectangle ABCD

Thus, D is correct.  The area of A'B'C'D' is 2.25 times the area of ABCD.