Question

a similarity transformation maps polygon abcd to polygon pqrs. if the length of ab is 6 and the length of the corresponding side, pq, is 12, what is the scale factor of dilation?
a. 2
b. 0.5
c. -6
d. 6
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Explanation:

Step1: Recall the formula for scale factor

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

Step2: Identify the image and pre - image segments

Here, the pre - image segment is \(\overline{AB}\) with length \(a = 6\), and the image segment is \(\overline{PQ}\) with length \(b=12\).

Step3: Calculate the scale factor

Substitute the values into the formula: \(k=\frac{b}{a}=\frac{12}{6}\).
Since \(\frac{12}{6}=2\).

Answer:

A. 2