Question

derek tried to dilate the isosceles trapezoid abdc with the center of dilation at the origin with a scale factor of 2. check his work and complete the statements. the slope of ac is dropdown. the slope of eg is dropdown. the polygons are not dilations of each other because dropdown.

Explanation:

Step1: Find coordinates of A and C

From the grid: A(-3,5), C(-3,0)

Step2: Calculate slope of AC

Slope formula: $\frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 5}{-3 - (-3)} = \frac{-5}{0}$ (undefined, vertical line)

Step3: Find coordinates of E and G

From the grid: E(-2,3), G(-2,1)

Step4: Calculate slope of EG

Slope formula: $\frac{1 - 3}{-2 - (-2)} = \frac{-2}{0}$ (undefined, vertical line)

Step5: Check dilation condition

Dilation preserves slopes, but corresponding sides should be scaled by factor 2. AC length is 5, EG length is 2 (not 10=5×2), so slopes are same but side lengths not scaled uniformly.

Answer:

The slope of AC is undefined.
The slope of EG is undefined.
The polygons are not dilations of each other because corresponding side lengths are not scaled by the same factor.