Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.

Explanation:

Step1: Identify original coordinates

$P(0, - 2)$, $Q(3,0)$, $R(0,1)$, $S(-3,0)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula is $(x,y)\to(kx,ky)$. Here $k = 3$.
For point $P(0,-2)$: $(0\times3,-2\times3)=(0,-6)$
For point $Q(3,0)$: $(3\times3,0\times3)=(9,0)$
For point $R(0,1)$: $(0\times3,1\times3)=(0,3)$
For point $S(-3,0)$: $(-3\times3,0\times3)=(-9,0)$

Answer:

$P'(0,-6)$, $Q'(9,0)$, $R'(0,3)$, $S'(-9,0)$