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

Explanation:

Step1: Identify original coordinates

$E(0, - 6)$, $F(8,-6)$, $G(8,3)$, $H(0,3)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k=\frac{1}{3}$, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x',y')=(k x,k y)$. For point $E(0, - 6)$: $x'=\frac{1}{3}\times0 = 0$, $y'=\frac{1}{3}\times(-6)=-2$. So $E'(0,-2)$. For point $F(8,-6)$: $x'=\frac{1}{3}\times8=\frac{8}{3}$, $y'=\frac{1}{3}\times(-6)=-2$. So $F'(\frac{8}{3},-2)$. For point $G(8,3)$: $x'=\frac{1}{3}\times8=\frac{8}{3}$, $y'=\frac{1}{3}\times3 = 1$. So $G'(\frac{8}{3},1)$. For point $H(0,3)$: $x'=\frac{1}{3}\times0 = 0$, $y'=\frac{1}{3}\times3 = 1$. So $H'(0,1)$.

Answer:

$E'(0,-2)$, $F'(\frac{8}{3},-2)$, $G'(\frac{8}{3},1)$, $H'(0,1)$