Question

Use the Polygon tool to draw the image of the given quadrilateral under a dilation with a scale

Answer 1

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:

$scale\ factor=\frac{2}{3}$

Since:

$0$

It is a Reduction.

You can identify that the vertices of the quadritaleral are:

$(-3,0),(-9,-3),(-6,-9),(3,-6)$

 So you need to multiply the coordinates of eac vertex by $\frac{2}{3}$ in order to get the coordinates of the image.

Then, you get:

$(\frac{(-3)(2)}{3},0*\frac{2}{3})=(-2,0)\\\\(\frac{(-9)(2)}{3}),\frac{(-3)(2)}{3})=(-6,-2)\\\\(\frac{(-6)(2)}{3},\frac{(-9)(2)}{3})=(-4,-6)\\\\(3*\frac{2}{3},\frac{(-6)(2)}{3})=(2,-4)$

Now you can plot the points and draw the image of the given quadrilateral.

See the picture attached.