trapezoid abcd was dilated to create trapezoid abcd. which statements are true about the trapezoids? select…

Explanation:

Step1: Calculate length of AD

Count the grid - units between points A and D. A is at x = - 4 and D is at x = 4. So, $AD=\vert4-( - 4)\vert = 8$ units.

Step2: Calculate length of A'D'

Count the grid - units between points A' and D'. A' is at x=-2 and D' is at x = 2. So, $A'D'=\vert2-( - 2)\vert = 4$ units.

Step3: Determine scale factor

The scale factor $k=\frac{A'D'}{AD}=\frac{4}{8}=\frac{1}{2}$. Since $k=\frac{1}{2}<1$, the image is smaller than the pre - image.

Step4: Calculate slope of CD and C'D'

For two points $(x_1,y_1)$ and $(x_2,y_2)$, the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let C=(2,2) and D=(4,2), slope of CD $m_{CD}=\frac{2 - 2}{4 - 2}=0$. Let C'=(1,1) and D'=(2,1), slope of C'D' $m_{C'D'}=\frac{1 - 1}{2 - 1}=0$.

Answer:

The length of side AD is 8 units. The length of side A'D' is 4 units. The scale factor is $\frac{1}{2}$.