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 coordinates of its image $(x',y')$ are given by $(kx,ky)$. Here $k = \frac{1}{4}$.

Step2: Find coordinates of point C

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

Step3: Find coordinates of point D

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

Step4: Find coordinates of point E

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

Step5: Find coordinates of point F

The coordinates of point F are $(-4,-4)$. Using the dilation formula, $x'=\frac{1}{4}\times(-4)=-1$ and $y'=\frac{1}{4}\times(-4)=-1$. So $F'(-1,-1)$.

Answer:

$C'(-2,-1)$
$D'(-2,0)$
$E'(-1,0)$
$F'(-1,-1)$