Question

trapezoid wxyz is the image of trapezoid wxyz under a dilation through point c. what scale factor was used in the dilation? -\frac{4}{3} -\frac{3}{4} \frac{3}{4} \frac{4}{3}

Explanation:

Step1: Recall dilation formula

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

Step2: Identify corresponding side lengths

We can use the lengths of \(\overline{W'X'}\) and \(\overline{WX}\). The length of \(\overline{WX} = 8m\) and the length of \(\overline{W'X'}=6m\).

Step3: Calculate the scale factor

\(k=\frac{W'X'}{WX}=\frac{6}{8}=\frac{3}{4}\). Also, since the image and pre - image have the same orientation (the trapezoids are not flipped in a non - orientation - preserving way), the scale factor is positive.

Answer:

C. \(\frac{3}{4}\)