Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of point $P$ are $(- 2,-2)$, of point $Q$ are $(-2,2)$, of point $R$ are $(2,2)$ and of point $S$ are $(2,-2)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 4$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(kx,ky)$.
For point $P(-2,-2)$:
$x'=4\times(-2)=-8$, $y'=4\times(-2)=-8$. So $P'(-8,-8)$.
For point $Q(-2,2)$:
$x'=4\times(-2)=-8$, $y'=4\times2 = 8$. So $Q'(-8,8)$.
For point $R(2,2)$:
$x'=4\times2=8$, $y'=4\times2 = 8$. So $R'(8,8)$.
For point $S(2,-2)$:
$x'=4\times2=8$, $y'=4\times(-2)=-8$. So $S'(8,-8)$.

Answer:

$P'(-8,-8)$, $Q'(-8,8)$, $R'(8,8)$, $S'(8,-8)$