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, $E(6,3)$, $F(6,9)$, $G(-6,9)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = \frac{1}{3}$, the formula for the coordinates of a point $(x,y)$ after dilation is $(kx,ky)$.
For point $E$:
$x_E'=\frac{1}{3}\times6 = 2$, $y_E'=\frac{1}{3}\times3 = 1$. So $E'(2,1)$.
For point $F$:
$x_F'=\frac{1}{3}\times6 = 2$, $y_F'=\frac{1}{3}\times9 = 3$. So $F'(2,3)$.
For point $G$:
$x_G'=\frac{1}{3}\times(-6)=-2$, $y_G'=\frac{1}{3}\times9 = 3$. So $G'(-2,3)$.

Answer:

$E'(2,1)$
$F'(2,3)$
$G'(-2,3)$