Question

did marge calculate the scale factor correctly?
why or why not?
no, because she tried to apply a scale factor of 6 but made a
mistake in her calculations.
no, because she did not use corresponding parts. she matched
side qr in the preimage to side pr in the image.
no, because the image was scaled up by a factor of 5.
yes, the image was correctly scaled up by a scale factor of 6
because she used corresponding parts.

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) is calculated as \(k=\frac{\text{length of a side in the image}}{\text{length of the corresponding side in the pre - image}}\).

Step2: Identify the corresponding sides

In the pre - image, side \(QR = 9\) and in the image, side \(QR = 60\).

Step3: Calculate the scale factor

Using the formula \(k=\frac{60}{9}=\frac{20}{3}\approx6.67\). Marge used \(QR\) in the pre - image (\(15\)) and \(QR\) in the image (\(60\)) which are not corresponding parts (the pre - image has \(QR = 9\) and \(PR = 15\), the image has \(QR = 60\) and \(PR = 60\)).

Answer:

No, because she did not use corresponding parts. She matched up side \(QR\) in the pre - image (\(15\)) to side \(PR\) in the image (\(60\)) instead of using the correct corresponding sides (e.g., \(QR\) pre - image \(=9\) and \(QR\) image \(=60\) or \(PR\) pre - image \(=15\) and \(PR\) image \(=60\)).