Question

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

Explanation:

Step1: Identify original coordinates

From the graph, we can see that the coordinates of point $A$ are $(-6,-8)$, point $B$ are $(-6, - 2)$, point $C$ are $(-2,8)$ and point $D$ are $(-2,-8)$.

Step2: Apply dilation formula

The formula for dilation centered at the origin with a scale - factor $k$ is $(x,y)\to(kx,ky)$. Here $k = \frac{1}{2}$.
For point $A(-6,-8)$:
$x_1=\frac{1}{2}\times(-6)=-3$, $y_1=\frac{1}{2}\times(-8)=-4$. The new coordinate of $A$ is $(-3,-4)$.
For point $B(-6,-2)$:
$x_2=\frac{1}{2}\times(-6)=-3$, $y_2=\frac{1}{2}\times(-2)=-1$. The new coordinate of $B$ is $(-3,-1)$.
For point $C(-2,8)$:
$x_3=\frac{1}{2}\times(-2)=-1$, $y_3=\frac{1}{2}\times8 = 4$. The new coordinate of $C$ is $(-1,4)$.
For point $D(-2,-8)$:
$x_4=\frac{1}{2}\times(-2)=-1$, $y_4=\frac{1}{2}\times(-8)=-4$. The new coordinate of $D$ is $(-1,-4)$.

Answer:

The new coordinates of $A$ are $(-3,-4)$, of $B$ are $(-3,-1)$, of $C$ are $(-1,4)$ and of $D$ are $(-1,-4)$.