Question

A rectangle on the coordinate plane has vertices at (0,0), (3,0), (3,2), and (0,2). A dialation of the rectangle has vertices at (0,0), (9,0), (9,6), and (0,1). Find the scale factor

Answer 1

Answer: The scale factor is 3.

Step-by-step explanation:

1. You kwnow that original rectangle has the following coordinates in its vertices:

 (0,0), (3,0), (3,2), and (0,2)

2. After dilation, the rectangle has vertices at (0,0), (9,0), (9,6), and (0,1). Therefore, you can calculate the scale factor as following:

Let's call $k$ the scale factor and let's choose one the coordinates of the original rectangle and the same coordinate after dilation:

Original vertex: (3,2) ; Vertex after dilation: (9,6)

Then:

$3k=9$

$k=3$

$2k=6$

$k=3$

The scale factor is 3.