write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{2}$, centered at the…

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, if a point has coordinates $(x,y)$, its image has coordinates $(kx,ky)$. Here $k = \frac{1}{2}$.

Step2: Find coordinates of point $S$

The coordinates of point $S$ are $(- 8,-10)$. After dilation, $x'=\frac{1}{2}\times(-8)=-4$ and $y'=\frac{1}{2}\times(-10)=-5$. So $S'(-4,-5)$.

Step3: Find coordinates of point $T$

The coordinates of point $T$ are $(-8,2)$. After dilation, $x'=\frac{1}{2}\times(-8)=-4$ and $y'=\frac{1}{2}\times2 = 1$. So $T'(-4,1)$.

Step4: Find coordinates of point $U$

The coordinates of point $U$ are $(4,2)$. After dilation, $x'=\frac{1}{2}\times4 = 2$ and $y'=\frac{1}{2}\times2=1$. So $U'(2,1)$.

Step5: Find coordinates of point $V$

The coordinates of point $V$ are $(4,-10)$. After dilation, $x'=\frac{1}{2}\times4 = 2$ and $y'=\frac{1}{2}\times(-10)=-5$. So $V'(2,-5)$.

Answer:

$S'(-4,-5)$ $T'(-4,1)$ $U'(2,1)$ $V'(2,-5)$