Question

△efg is the image of △efg under a dilation through point c what scale factor was used in the dilation? -2 -1/2 1/2 2

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of a side in image}}{\text{length of corresponding side in original figure}}\)

Step2: Identify corresponding side lengths

The length of a side in \(\triangle E'F'G'\) is \(4\) cm and the length of the corresponding side in \(\triangle EFG\) is \(8\) cm. Also, note the orientation (the image is on the opposite side of the center of dilation \(C\) compared to the original, so the scale factor is negative)

Step3: Calculate the scale factor

\(k =-\frac{4}{8}=-\frac{1}{2}\)

Answer:

B. \(-\frac{1}{2}\)