How can you model the effect of a dilation by a scale factor of 3 on the area of a two-dimensional shape?(1 point)

Responses

The area will be 9 times as great.

The area will be 1 1/2 times as great.

The area will be 6 times as great.

The area will be 3 times as great.

1 answer

When a two-dimensional shape is dilated by a scale factor \( k \), the area of the shape scales by a factor of \( k^2 \).

In this case, the scale factor \( k \) is 3. Therefore, the area will be scaled by \( 3^2 = 9 \).

So, the correct response is:

The area will be 9 times as great.