Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify original coordinates

$R(-2,-2)$, $S(-2,3)$, $T(2,3)$, $U(2,-2)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 3$, the formula is $(x,y)\to(kx,ky)$.
For point $R$: $x=-2,y = - 2$, new coordinates are $(3\times(-2),3\times(-2))=(-6,-6)$
For point $S$: $x=-2,y = 3$, new coordinates are $(3\times(-2),3\times3)=(-6,9)$
For point $T$: $x = 2,y = 3$, new coordinates are $(3\times2,3\times3)=(6,9)$
For point $U$: $x = 2,y=-2$, new coordinates are $(3\times2,3\times(-2))=(6,-6)$

Answer:

$R'(-6,-6)$, $S'(-6,9)$, $T'(6,9)$, $U'(6,-6)$