Question

find the scale factor used for the dilation between the similar figures.
a. 3/2
b. 1/2
c. 2

Explanation:

Step1: Determine the length of a side of the original and dilated rectangle

Assume the side - length of the smaller (original) rectangle: count the units on the coordinate grid. Let's say the side - length of the smaller rectangle \(s_1\). If we consider the vertical sides, for example, if the smaller rectangle has a vertical side from \(y = 4\) to \(y = 8\), \(s_1=4\) units.
The side - length of the larger (dilated) rectangle \(s_2\). If the larger rectangle has a vertical side from \(y = 0\) to \(y = 8\), \(s_2 = 8\) units.

Step2: Use the scale - factor formula

The scale factor \(k\) for a dilation is given by the formula \(k=\frac{\text{length of a side of the dilated figure}}{\text{length of the corresponding side of the original figure}}\).
Substitute \(s_1 = 4\) and \(s_2=8\) into the formula: \(k=\frac{s_2}{s_1}\).

$$k=\frac{8}{4}=2$$

Answer:

C. 2