Question

test prep dilate abcd with a scale factor of 2 and center (0, 0). use the polygon tool to plot the image.

Explanation:

Step1: Recall dilation formula

If the center of dilation is at the origin $(0,0)$ and the scale - factor is $k$, the coordinates of a point $(x,y)$ after dilation become $(kx,ky)$.

Step2: Identify the vertices of the original polygon

The vertices of the trapezoid $ABCD$ are $A(-2,2)$, $B(1,2)$, $C(2, - 1)$, $D(-2,-1)$.

Step3: Apply the dilation formula

For point $A(-2,2)$ with $k = 2$, the new coordinates are $A'=(-2\times2,2\times2)=(-4,4)$.
For point $B(1,2)$ with $k = 2$, the new coordinates are $B'=(1\times2,2\times2)=(2,4)$.
For point $C(2,-1)$ with $k = 2$, the new coordinates are $C'=(2\times2,-1\times2)=(4,-2)$.
For point $D(-2,-1)$ with $k = 2$, the new coordinates are $D'=(-2\times2,-1\times2)=(-4,-2)$.

Answer:

The vertices of the dilated polygon are $A'(-4,4)$, $B'(2,4)$, $C'(4,-2)$, $D'(-4,-2)$. Plot these points using the polygon tool.