Question

1. a rectangle with vertices p(1,1), q(3,1), r(3,4), and s(1,4) is dilated to p(2,2), q(6,2), r(6,8), and s(2,8). what is the dilation factor?

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

Explanation:

Step1: Recall dilation - factor formula

The dilation factor $k$ for a point $(x,y)$ dilated to $(x',y')$ with respect to the origin (if no center - of - dilation is specified, we assume origin) is given by $k=\frac{x'}{x}=\frac{y'}{y}$ for non - zero $x$ and $y$. Let's use the $x$ - coordinates of one of the points.

Step2: Select a point and calculate

Let's take point $P(1,1)$ which is dilated to $P'(2,2)$. Using the formula for the dilation factor based on $x$ - coordinates, $k = \frac{x_{P'}}{x_{P}}$. Here, $x_{P}=1$ and $x_{P'}=2$. So, $k=\frac{2}{1}=2$.

Answer:

2