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

Explanation:

Step1: Find the coordinates of points

From the graph, \(A(-3, 4)\), \(C(-4,0)\), \(E(-2,3)\), \(G(-1,0)\)

Step2: Calculate the slope of \(AC\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(A(-3,4)\) and \(C(-4,0)\), \(m_{AC}=\frac{0 - 4}{-4+ 3}=\frac{-4}{-1}=4\)

Step3: Calculate the slope of \(EG\)

For points \(E(-2,3)\) and \(G(-1,0)\), \(m_{EG}=\frac{0 - 3}{-1 + 2}=\frac{-3}{1}=-3\)

Step4: Analyze dilation property

In a dilation with center at the origin, if the scale factor is \(k = 2\), the slope of corresponding line segments should be equal. Since \(m_{AC}
eq m_{EG}\), the polygons are not dilations of each other.

Answer:

The slope of \(AC\) is \(4\). The slope of \(EG\) is \(-3\). The polygons are not dilations of each other because the slopes of corresponding line segments are not equal.