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

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

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 4$, if a point has original coordinates $(x,y)$, the new coordinates $(x',y')$ are given by $(x',y')=(kx,ky)$.
For point $P$: $x'=4\times(-2)=-8$, $y'=4\times(-2)=-8$, so $P'(-8,-8)$
For point $Q$: $x'=4\times(-2)=-8$, $y'=4\times2 = 8$, so $Q'(-8,8)$
For point $R$: $x'=4\times2=8$, $y'=4\times2 = 8$, so $R'(8,8)$
For point $S$: $x'=4\times2=8$, $y'=4\times(-2)=-8$, so $S'(8,-8)$

Answer:

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