Question

ΔDEF undergoes a dilation, with a scale factor of 4, to form ΔD'E'F'. Side D'E' is 4 times the length of side DE. What is the area of ΔD'E'F', compared to the area of ΔDEF?

A.The area of ΔD'E'F' is 4 times the area of ΔDEF.
B. The area of ΔD'E'F' is 1/16th of the area of ΔDEF.
C. The area of ΔD'E'F' is 16 times the area of ΔDEF.
D.The area of ΔD'E'F' is 1/4 of the area of ΔDEF.

Answer 1

The area of ΔD'E'F' is 16 times the area of ΔDEF.

Step-by-step explanation:

The area of ΔD'E'F' is 16 times the area of ΔDEF.

To find the area ratio, we need to square the scale factor of 4. 4*4 = 16. So, the area of ΔD'E'F' is 16 times the area of ΔDEF.When ΔDEF undergoes a dilation to form ΔD'E'F' with a scale factor of 4, the lengths of corresponding sides are quadrupled. However, the area will increase by the square of the scale factor. Since the scale factor is 4, the area of ΔD'E'F' is 42, or 16 times the area of ΔDEF. Therefore, the correct answer is C. The area of ΔD'E'F' is 16 times the area of ΔDEF.