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

$S(-3,-1)$, $T(0, - 1)$, $U(0,3)$, $V(-3,3)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 3$, the formula is $(x,y)\to(kx,ky)$.
For point $S(-3,-1)$: $( - 3\times3,-1\times3)=(-9,-3)$
For point $T(0,-1)$: $(0\times3,-1\times3)=(0,-3)$
For point $U(0,3)$: $(0\times3,3\times3)=(0,9)$
For point $V(-3,3)$: $(-3\times3,3\times3)=(-9,9)$

Answer:

The new coordinates are $S'(-9,-3)$, $T'(0,-3)$, $U'(0,9)$, $V'(-9,9)$