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? a. 1/2 b. 3/2 c. 2 d. 4 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? a. 1/3 b. 2/3 c. d.

Explanation:

Step1: Select a corresponding side

Let's consider side WX of rectangle WXYZ and side W'X' of rectangle W'X'Y'Z'. The length of side WX can be found by counting the grid - squares. W(3,2) and X(5,4), using the distance formula for horizontal and vertical segments (since it's a rectangle on a grid), the length of WX is 2 units. The length of side W'X' with W'(6,4) and X'(10,8) is 4 units.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of the image segment to the length of the pre - image segment. So, \(k=\frac{\text{length of W'X'}}{\text{length of WX}}=\frac{4}{2} = 2\).

Answer:

C. 2