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

$S(-2, - 2)$, $T(0, - 2)$, $U(2,2)$, $V(-2,2)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 4$, the formula to find the new coordinates $(x',y')$ from the original coordinates $(x,y)$ is $(x',y')=(k\cdot x,k\cdot y)$.
For point $S$: $x=-2,y = - 2$, so $S'=(4\times(-2),4\times(-2))=(-8,-8)$
For point $T$: $x = 0,y=-2$, so $T'=(4\times0,4\times(-2))=(0,-8)$
For point $U$: $x = 2,y = 2$, so $U'=(4\times2,4\times2)=(8,8)$
For point $V$: $x=-2,y = 2$, so $V'=(4\times(-2),4\times2)=(-8,8)$

Answer:

$S'(-8,-8),T'(0,-8),U'(8,8),V'(-8,8)$