Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{4}$, centered at the origin.

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor $k$, if a point has coordinates $(x,y)$, the new coordinates $(x',y')$ after dilation are given by $(x',y')=(k x,k y)$. Here $k = \frac{1}{4}$.

Step2: Find coordinates of point $D$

The coordinates of point $D$ are $(8,0)$. After dilation, $x'=\frac{1}{4}\times8 = 2$ and $y'=\frac{1}{4}\times0 = 0$. So the new coordinates of $D$ are $(2,0)$.

Step3: Find coordinates of point $C$

The coordinates of point $C$ are $(8, - 4)$. After dilation, $x'=\frac{1}{4}\times8 = 2$ and $y'=\frac{1}{4}\times(-4)=-1$. So the new coordinates of $C$ are $(2,-1)$.

Step4: Find coordinates of point $E$

The coordinates of point $E$ are $(0, - 4)$. After dilation, $x'=\frac{1}{4}\times0 = 0$ and $y'=\frac{1}{4}\times(-4)=-1$. So the new coordinates of $E$ are $(0,-1)$.

Answer:

The new coordinates of $D$ are $(2,0)$, of $C$ are $(2,-1)$, and of $E$ are $(0,-1)$.