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

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 $\frac{1}{2}$.

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 $\frac{1}{2}$.

Answer

Explanation:

Step1: Calculate length of AD

Count the grid - units from point A to point D. A is at x = - 4 and D is at x = 4. The length of AD is (|4-(-4)|=8) units.

Step2: Analyze side A'D'

Since the trapezoid is dilated with a scale - factor of (\frac{1}{2}), if AD = 8 units, then (A'D'=\frac{1}{2}\times AD=\frac{1}{2}\times8 = 4) units.

Step3: Determine scale - factor and size comparison

The distance between corresponding points of the pre - image and image is halved. So the scale factor is (\frac{1}{2}), and the image is smaller than the pre - image.

Step4: Calculate slopes of CD and C'D'

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). For CD, if C(2,1) and D(4,0), then (m_{CD}=\frac{0 - 1}{4 - 2}=-\frac{1}{2}). For C'(1,\frac{1}{2}) and D'(2,0), (m_{C'D'}=\frac{0-\frac{1}{2}}{2 - 1}=-\frac{1}{2}).

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}).