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

$Q(-2,-2)$, $R(-2,2)$, $S(2,-2)$

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 $(x',y')=(k\cdot x,k\cdot y)$.
For point $Q$:
$x'_Q=4\times(-2)=-8$, $y'_Q=4\times(-2)=-8$
For point $R$:
$x'_R=4\times(-2)=-8$, $y'_R=4\times2 = 8$
For point $S$:
$x'_S=4\times2=8$, $y'_S=4\times(-2)=-8$

Answer:

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