Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{2}$, centered at the origin.
s(
t(
u(
v(

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 after dilation has coordinates $(kx,ky)$. Here $k = \frac{1}{2}$.

Step2: Identify original coordinates of point S

From the graph, the coordinates of point $S$ are $(4, - 6)$. After dilation, $x'=\frac{1}{2}\times4 = 2$ and $y'=\frac{1}{2}\times(-6)=-3$. So $S'=(2,-3)$.

Step3: Identify original coordinates of point T

The coordinates of point $T$ are $(10,2)$. After dilation, $x'=\frac{1}{2}\times10 = 5$ and $y'=\frac{1}{2}\times2 = 1$. So $T'=(5,1)$.

Step4: Identify original coordinates of point U

The coordinates of point $U$ are $(4,10)$. After dilation, $x'=\frac{1}{2}\times4 = 2$ and $y'=\frac{1}{2}\times10 = 5$. So $U'=(2,5)$.

Step5: Identify original coordinates of point V

The coordinates of point $V$ are $(-10,2)$. After dilation, $x'=\frac{1}{2}\times(-10)=-5$ and $y'=\frac{1}{2}\times2 = 1$. So $V'=(-5,1)$.

Answer:

$S'(2,-3)$
$T'(5,1)$
$U'(2,5)$
$V'(-5,1)$