Question

1. if a rectangle is dilated by a scale factor of 3, what happens to its area? a. the area stays the same b. the area triples c. the area is multiplied by 9 d. the area is divided by 3

Explanation:

Step1: Recall area - dilation relationship

The area of a two - dimensional shape after dilation by a scale factor \(k\) is given by \(A'=k^{2}A\), where \(A\) is the original area and \(A'\) is the new area.

Step2: Identify the scale factor

Here, the scale factor \(k = 3\).

Step3: Calculate the new area

Substitute \(k = 3\) into the formula \(A'=k^{2}A\). We get \(A'=3^{2}A=9A\).

Answer:

C. The area is multiplied by 9