Question

If DEF is dilated by a scale factor of 4, which statement is true of the image D'E'F' ?

1) m 2) 4(m 3) 4(D’E’) = DE
4) E'F' = 4(EF)

Answer 1

The correct statement for a figure DEF dilated by a scale factor of 4 is that side E'F' of the image D'E'F' will be four times the length of side EF.

Step-by-step explanation:

When a figure DEF is dilated by a scale factor of 4, the lengths of the sides of the image D'E'F' will be four times the length of the corresponding sides of the original figure DEF. Therefore, the true statement about the image D'E'F' is option 4: E'F' = 4(EF). This means that the length of side E'F' in the enlarged figure will be 4 times the length of side EF in the original figure.

In a dilation, all the side lengths of the original figure are multiplied by the scale factor to obtain the corresponding side lengths of the image. Here, each side length of DEF is multiplied by 4 to get the corresponding side length of D'E'F'.

So, statement 1) m is true because the side lengths of the image are 4 times the side lengths of the original figure.