Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{3}$, centered at the origin.
e(□,□)
f(□,□)
g(□,□)
h(□,□)

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 $k=\frac{1}{3}$, if a point has coordinates $(x,y)$, the new coordinates $(x',y')$ are given by $(x',y')=(k x,k y)$.
For point $E$: $x'_E=\frac{1}{3}\times0 = 0,y'_E=\frac{1}{3}\times(-6)=-2$
For point $F$: $x'_F=\frac{1}{3}\times8=\frac{8}{3},y'_F=\frac{1}{3}\times(-6)=-2$
For point $G$: $x'_G=\frac{1}{3}\times8=\frac{8}{3},y'_G=\frac{1}{3}\times3 = 1$
For point $H$: $x'_H=\frac{1}{3}\times0 = 0,y'_H=\frac{1}{3}\times3 = 1$

Answer:

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