Question

graph the image of parallelogram stuv after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

From the graph:
$S(-1, -3)$, $T(1, -3)$, $U(1, 2)$, $V(-1, 2)$

Step2: Apply dilation rule

Dilation center origin, scale factor 4: $(x,y)\to(4x,4y)$
$S' = 4\times(-1, -3) = (-4, -12)$
$T' = 4\times(1, -3) = (4, -12)$
$U' = 4\times(1, 2) = (4, 8)$
$V' = 4\times(-1, 2) = (-4, 8)$

Step3: Plot new points

Graph $S'(-4,-12)$, $T'(4,-12)$, $U'(4,8)$, $V'(-4,8)$ and connect.

Answer:

The image of parallelogram STUV after dilation has vertices at $(-4, -12)$, $(4, -12)$, $(4, 8)$, and $(-4, 8)$. Plot these points and connect them to form the dilated parallelogram.