Question

If a shape is dilated by a scale factor of 4, what is the resulting area of the image?A.) The same as thearea of thepreimageB.) The new area is 3times larger thanthe preimageC.) The new area is 4times that of thepreimageD.) The new area is 16times larger thanthe preimage

Answer 1

The new area will be 16 times larger than the preimage.

Step-by-step explanation

The shape is dilated by a scale factor of 4.

When a shape is dilated, the area of the image changes quadratically.

This means that if a shape is dilated by a factor of k, the area of the image will become k^2 of the preimage.

Therefore, the area of the shape dilated by a scale factor of 4, will change by:

4^2 = 4 * 4 = 16

The new area will be 16 times larger than the preimage.

Option D is the answer.