Question

HELP!!! I'm struggling in this class could you please help a person out?

Answer 1

Answer:

Options (2) and (3)

Step-by-step explanation:

Rigid transformation like translation, rotation or reflection form the image with no change in the area or shape.

By applying dilation, area of the image shape gets dilated by the scale factor 'k'.

If k > 1, area of the image will be greater than the original shape.

If 0 < k < 1, are of the image will be smaller than the original.

Option (1),

There is a dilation by a scale factor of $\frac{2}{3}$ and $0$,

Therefore, image will be smaller than the original.

Option (2)

There are two dilations.

First dilation is by a scale factor of 2 and the second is by a scale factor of $\frac{2}{3}$.

By first dilation area of the image will get doubled.

Followed by the dilation by a scale factor of $\frac{2}{3}$, area of the image will be dilated by the scale factor = $2\times \frac{2}{3}$

                                         = $\frac{4}{3}$

Since, $\frac{4}{3}>1$, image will be greater than the original.

Option (3)

In this option polygon is dilated by a scale factor $\frac{3}{2}$.

Since, $\frac{3}{2}>1$

Image will have the greater area than the original.

Option (4)

In this option polygon is dilated by a scale factor $\frac{1}{2}$.

Therefore, area of the image will be less than the area of the original.

Options (2) and (3) will be the correct options.