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 the slope of eg is the polygons are not dilations of each other because the center of dilation is not at (0,0) the coordinate g should be at (-1,0) the corresponding sides are not parallel ac and eg are corresponding sides

Explanation:

Step1: Find the slope of \(AC\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(A(-3,4)\) and \(C(-4,0)\), \(m_{AC}=\frac{4 - 0}{-3+4}=4\)

Step2: Find the slope of \(EG\)

For points \(E(-1,2)\) and \(G(-2,0)\), \(m_{EG}=\frac{2 - 0}{-1 + 2}=2\)

Step3: Analyze the reason for non - dilation

In a dilation, corresponding sides are parallel (i.e., have the same slope). Since \(m_{AC}
eq m_{EG}\), the corresponding sides are not parallel.

Answer:

The slope of \(AC\) is \(4\). The slope of \(EG\) is \(2\). The polygons are not dilations of each other because the corresponding sides are not parallel.