Question

preimage image scale factor = 4 9 × 4 = 36 did christy calculate the scale factor correctly? why or why not? no, the image was scaled up by a factor of 5 yes, the image was correctly scaled up by a scale factor of 4 because she used corresponding parts. no, because she did not use corresponding parts. she matched up side gi in the preimage to side gh in the image. no, because she tried to apply a scale factor of 4 but made a mistake in her calculations. before you continue, we recommend completing the day 2 activity, \what goes together?\

Explanation:

Step1: Recall the concept of scale factor

The scale factor is calculated by dividing the length of a side in the image by the length of the corresponding side in the pre - image.

Step2: Identify corresponding sides

In the pre - image, side \(GH = 9\). In the image, the corresponding side should be the base of the image triangle. But Christy matched \(GH\) (a side of the pre - image triangle) with \(GI\) (a non - corresponding side of the image triangle). The correct corresponding side for \(GH\) (pre - image base) is the base of the image triangle. If we consider the correct corresponding sides (base of pre - image \(=9\), base of image \( = 36\)), the scale factor \(k=\frac{36}{9}=4\). But Christy made a mistake in choosing corresponding sides. She matched \(GI\) (pre - image side \(=36\)) with \(GH\) (image side \(=36\)) which is incorrect.

Answer:

No, because she did not use corresponding parts. She matched up side \(GI\) in the preimage to side \(GH\) in the image.