Question

write the coordinates of the vertices after a dilation with a scale factor of 1/5, centered at the origin.

Explanation:

Step1: Identify original coordinates

$Q=(0,-10)$; $R=(10,0)$; $S=(0,10)$; $T=(-4,0)$

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 $(x',y')=(kx,ky)$.
For point $Q(0,-10)$:
$x'=\frac{1}{5}\times0 = 0$, $y'=\frac{1}{5}\times(-10)=-2$, so $Q'=(0, - 2)$
For point $R(10,0)$:
$x'=\frac{1}{5}\times10 = 2$, $y'=\frac{1}{5}\times0 = 0$, so $R'=(2,0)$
For point $S(0,10)$:
$x'=\frac{1}{5}\times0 = 0$, $y'=\frac{1}{5}\times10 = 2$, so $S'=(0,2)$
For point $T(-4,0)$:
$x'=\frac{1}{5}\times(-4)=-\frac{4}{5}$, $y'=\frac{1}{5}\times0 = 0$, so $T'=(-\frac{4}{5},0)$

Answer:

$Q'=(0, - 2)$; $R'=(2,0)$; $S'=(0,2)$; $T'=(-\frac{4}{5},0)$