Question

The vertices of a rectangle are located at Q(-5, 1), R(-5, 3), S(1, 3), and T(-1, 1). The rectangle is dilated. The new coordinates are Q'(-15, 3), R'(-15, 9), S'(-3, 9), and T'(-3, 3). What scale factor was used?

a) 2
b) 3
c) 4
d) 5

Answer 1

The scale factor used in the dilation of the rectangle, determined by comparing the coordinates of vertex Q before and after dilation, is 3.The correct option is B.

Step-by-step explanation:

To find the scale factor used in the dilation of a rectangle, we can compare the coordinates of a vertex before and after the transformation. Let's look at the vertex Q. Initially, Q is located at (-5, 1), and after dilation, it is located at Q'(-15, 3). To find the scale factor, we compare the x-coordinates and the y-coordinates separately.

For the x-coordinate, the original coordinate of Q is -5, and after dilation, the coordinate of Q' is -15. If we divide the dilated x-coordinate by the original x-coordinate we get:

Scale factor for x = -15 / -5 = 3

For the y-coordinate, the original coordinate of Q is 1, and after dilation, the coordinate of Q' is 3. Dividing the dilated y-coordinate by the original y-coordinate we get:

Scale factor for y = 3 / 1 = 3

Since the scale factors for both coordinates are the same, the overall scale factor used in dilating the rectangle is 3, which corresponds to option b).