Question

the trapezoid fghj is a dilation of the trapezoid fghi. what is the scale factor of the dilation? 1/2

Explanation:

Step1: Identify corresponding sides

Let's consider the vertical side \(GH\) and \(G'H'\). The length of \(GH\) is \(8 - 4=4\) units (since \(G\) has \(y\) - coordinate \(8\) and \(H\) has \(y\) - coordinate \(4\)). The length of \(G'H'\) is \(4 - 2 = 2\) units (since \(G'\) has \(y\) - coordinate \(4\) and \(H'\) has \(y\) - coordinate \(2\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of the image segment}}{\text{length of the pre - image segment}}\). So, \(k=\frac{G'H'}{GH}\). Substituting the values, we get \(k=\frac{2}{4}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)