Question

trapezoid abcd was dilated to create trapezoid abcd.
which statements are true about the trapezoids? select three options.
the length of side ad is 8 units.
the length of side ad is 4 units.
the image is larger than the pre - image.
sides cd and cd both have the same slope, 2.
the scale factor is \\(\frac{1}{2}\\).

Explanation:

Step1: Find coordinates of points

A(-4,0), D(4,0), A'(-2,0), D'(2,0), C(2,2), C'(1,1)

Step2: Calculate AD length

AD = |4 - (-4)| = 8 units (True)

Step3: Calculate A'D' length

A'D' = |2 - (-2)| = 4 units (True)

Step4: Check image size

A'D' < AD → image smaller (False)

Step5: Calculate slopes of CD and C'D'

Slope CD: $\frac{2-0}{2-4}=-1$; Slope C'D': $\frac{1-0}{1-2}=-1$ (False)

Step6: Find scale factor

Scale factor = $\frac{A'D'}{AD}=\frac{4}{8}=\frac{1}{2}$ (True)

Answer:

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