Question

rectangle pqrs is dilated about the origin to form pqrs.
· point p has coordinates (2, 0.5).
· point p has coordinates (8, 2).
· the perimeter of pqrs is 16.
what is the perimeter of pqrs?
a. 16
b. 24
c. 32
d. 64

Explanation:

Step1: Find the dilation factor

The dilation factor $k$ for the $x$-coordinates (or $y$-coordinates) can be found by dividing the $x$-coordinate of $P'$ by the $x$-coordinate of $P$. So $k=\frac{8}{2} = 4$.

Step2: Use the property of dilation for perimeter

When a figure is dilated by a factor $k$, the perimeter of the dilated figure is $k$ times the perimeter of the original figure. Given the perimeter of $PQRS$ is $16$ and $k = 4$, the perimeter of $P'Q'R'S'$ is $16\times4$.
$16\times4=64$

Answer:

D. 64