Question

polygon abcd, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image abcd. the slope of \\( \overline { c ^ { prime } d ^ { prime } } \\) is

Explanation:

Step1: Find coordinates of \(C\) and \(D\)

From the graph, \(C=(5,5)\) and \(D=(2,4)\).

Step2: Recall the property of dilation

Dilation preserves the slope. The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step3: Calculate the slope of \(\overline{CD}\)

Let \((x_1,y_1)=(2,4)\) and \((x_2,y_2)=(5,5)\). Then \(m=\frac{5 - 4}{5 - 2}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)