Question

trapezoid ( wxyz ) is the image of trapezoid ( wxyz ) under a dilation through point ( c ). what scale factor was used in the dilation? ( -\frac{7}{3} ) ( -\frac{3}{7} ) ( \frac{3}{7} ) ( \frac{7}{3} )

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of a segment in the image}}{\text{length of the corresponding segment in the pre - image}}\)

Step2: Identify the corresponding segments

Let's consider the segments \(ZW\) and \(Z'W'\). The length of \(ZW = 14\) units and the length of \(Z'W'=6\) units.

Step3: Calculate the scale factor

Using the formula \(k=\frac{Z'W'}{ZW}\), substitute \(Z'W' = 6\) and \(ZW = 14\). So \(k=\frac{6}{14}=\frac{3}{7}\). Also, since the image is smaller than the pre - image and the dilation is through a point (not a reflection, so no negative sign as the orientation is the same in terms of direction from the center of dilation), we take the positive value.

Answer:

C. \(\frac{3}{7}\)