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:
![scale\ factor=\frac{2}{3}](https://tex.z-dn.net/?f=scale%5C%20factor%3D%5Cfrac%7B2%7D%7B3%7D)
Since:
![0](https://tex.z-dn.net/?f=0%3C%5Cfrac%7B2%7D%7B3%7D%3C1)
It is a Reduction.
You can identify that the vertices of the quadritaleral are:
![(-3,0),(-9,-3),(-6,-9),(3,-6)](https://tex.z-dn.net/?f=%28-3%2C0%29%2C%28-9%2C-3%29%2C%28-6%2C-9%29%2C%283%2C-6%29)
So you need to multiply the coordinates of eac vertex by
in order to get the coordinates of the image.
Then, you get:
![(\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)](https://tex.z-dn.net/?f=%28%5Cfrac%7B%28-3%29%282%29%7D%7B3%7D%2C0%2A%5Cfrac%7B2%7D%7B3%7D%29%3D%28-2%2C0%29%5C%5C%5C%5C%28%5Cfrac%7B%28-9%29%282%29%7D%7B3%7D%29%2C%5Cfrac%7B%28-3%29%282%29%7D%7B3%7D%29%3D%28-6%2C-2%29%5C%5C%5C%5C%28%5Cfrac%7B%28-6%29%282%29%7D%7B3%7D%2C%5Cfrac%7B%28-9%29%282%29%7D%7B3%7D%29%3D%28-4%2C-6%29%5C%5C%5C%5C%283%2A%5Cfrac%7B2%7D%7B3%7D%2C%5Cfrac%7B%28-6%29%282%29%7D%7B3%7D%29%3D%282%2C-4%29)
Now you can plot the points and draw the image of the given quadrilateral.
See the picture attached.