Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{3}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

From the graph, $R(-9,0)$, $S(9,0)$, $T(0,6)$, $U(-6,6)$.

Step2: Apply dilation formula

For a dilation with scale - factor $k = \frac{1}{3}$ centered at the origin $(x,y)\to(kx,ky)$.
For point $R$: $x=-9,y = 0$, new coordinates are $(\frac{1}{3}\times(-9),\frac{1}{3}\times0)=(-3,0)$.
For point $S$: $x = 9,y = 0$, new coordinates are $(\frac{1}{3}\times9,\frac{1}{3}\times0)=(3,0)$.
For point $T$: $x = 0,y = 6$, new coordinates are $(\frac{1}{3}\times0,\frac{1}{3}\times6)=(0,2)$.
For point $U$: $x=-6,y = 6$, new coordinates are $(\frac{1}{3}\times(-6),\frac{1}{3}\times6)=(-2,2)$.

Answer:

$R'(-3,0)$
$S'(3,0)$
$T'(0,2)$
$U'(-2,2)$