Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{5}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

$P(0, - 10)$, $Q(0,5)$, $R(5,5)$, $S(5,-10)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k=\frac{1}{5}$, if a point has coordinates $(x,y)$, the new coordinates $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$.
For point $P(0, - 10)$:
$x'=\frac{1}{5}\times0 = 0$, $y'=\frac{1}{5}\times(-10)=-2$. So $P'(0,-2)$
For point $Q(0,5)$:
$x'=\frac{1}{5}\times0 = 0$, $y'=\frac{1}{5}\times5 = 1$. So $Q'(0,1)$
For point $R(5,5)$:
$x'=\frac{1}{5}\times5 = 1$, $y'=\frac{1}{5}\times5 = 1$. So $R'(1,1)$
For point $S(5,-10)$:
$x'=\frac{1}{5}\times5 = 1$, $y'=\frac{1}{5}\times(-10)=-2$. So $S'(1,-2)$

Answer:

$P'(0,-2)$
$Q'(0,1)$
$R'(1,1)$
$S'(1,-2)$