Answer: See the picture attached.
Step-by-step explanation:
A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.
When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".
When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".
In this case we know that the scale factor is:
[tex]scale\ factor=\frac{2}{3}[/tex]
Since:
[tex]0<\frac{2}{3}<1[/tex]
It is a Reduction.
You can identify that the vertices of the quadritaleral are:
[tex](-3,0),(-9,-3),(-6,-9),(3,-6)[/tex]
So you need to multiply the coordinates of eac vertex by [tex]\frac{2}{3}[/tex] in order to get the coordinates of the image.
Then, you get:
[tex](\frac{(-3)(2)}{3},0*\frac{2}{3})=(-2,0)\\\\(\frac{(-9)(2)}{3}),\frac{(-3)(2)}{3})=(-6,-2)\\\\(\frac{(-6)(2)}{3},\frac{(-9)(2)}{3})=(-4,-6)\\\\(3*\frac{2}{3},\frac{(-6)(2)}{3})=(2,-4)[/tex]
Now you can plot the points and draw the image of the given quadrilateral.
See the picture attached.
