Question

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

Explanation:

Step1: Identify original coordinates

Assume the coordinates of point $R$ are $(- 8,-8)$, point $S$ are $(-8,8)$ and point $T$ are $(0,-8)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k=\frac{1}{4}$, if the original point has coordinates $(x,y)$, the new coordinates $(x',y')$ are given by $(x',y')=(k x,k y)$.
For point $R(-8,-8)$:
$x'_R=\frac{1}{4}\times(-8)=-2$
$y'_R=\frac{1}{4}\times(-8)=-2$
For point $S(-8,8)$:
$x'_S=\frac{1}{4}\times(-8)=-2$
$y'_S=\frac{1}{4}\times8 = 2$
For point $T(0,-8)$:
$x'_T=\frac{1}{4}\times0 = 0$
$y'_T=\frac{1}{4}\times(-8)=-2$

Answer:

The new coordinates of $R$ are $(-2,-2)$, of $S$ are $(-2,2)$ and of $T$ are $(0,-2)$.