Question

1. rectangle wxyz is the image of rectangle wxyz after a dilation. the center of dilation is the origin. what is the scale factor of the dilation? 2. triangle nop below will be dilated 3. rectangle abcd is the image of rectangle abcd after a dilation. the center of dilation is the origin. what is the scale factor of the dilation? 4. triangle rst below will be dilated with origin as the center of dilation and a scale factor of a. 1/2 b. 3/2 c. 2 d. 4 a. 1/3 b. 2/3 c. 2 d. 3

Explanation:

1.

Step1: Identify corresponding side lengths

Let's take one - side of the original rectangle and its corresponding side in the dilated rectangle. For example, if we consider the horizontal side of rectangle \(WXYZ\). Suppose the length of a horizontal side of rectangle \(WXYZ\) is \(2\) (counting the grid - units), and the length of the corresponding horizontal side of rectangle \(W'X'Y'Z'\) is \(4\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, \(k=\frac{\text{length of side in dilated figure}}{\text{length of side in original figure}}=\frac{4}{2} = 2\).

Step1: Identify corresponding side lengths

Take a side of rectangle \(ABCD\) and its corresponding side in rectangle \(A'B'C'D'\). Let's say the length of a vertical side of rectangle \(ABCD\) is \(1\) (counting the grid - units), and the length of the corresponding vertical side of rectangle \(A'B'C'D'\) is \(3\).

Step2: Calculate the scale factor

The scale factor \(k\) of the dilation is \(k=\frac{\text{length of side in dilated figure}}{\text{length of side in original figure}}=\frac{3}{1}=3\).

Answer:

C. 2

3.