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

• Coordinates of \(A(-3, 4)\) and \(C(-4, 0)\).
• Coordinates of \(E(-2, 2)\) and \(G(-2, 0)\).

Step2: Calculate the slope of \(AC\)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), for \(A(-3, 4)\) and \(C(-4, 0)\):
\(m_{AC}=\frac{0 - 4}{-4+ 3}=\frac{-4}{-1}=\frac{2}{3}\)

Step3: Calculate the slope of \(EG\)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), for \(E(-2, 2)\) and \(G(-1, 0)\):
\(m_{EG}=\frac{0 - 2}{-1 + 2}=\frac{-2}{1}=\frac{2}{1}\)

Step4: Check dilation property

In a dilation, corresponding segments should be parallel (i.e., have equal slopes). Since \(m_{AC}
eq m_{EG}\), the polygons are not dilations of each other.

Answer:

The slope of \(AC\) is \(\frac{2}{3}\). The slope of \(EG\) is \(\frac{2}{1}\). The polygons are not dilations of each other because the slopes of corresponding segments are not equal.