Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.
r(
s(
t(
u(

Explanation:

Step1: Identify original coordinates

From the graph, $R(0, - 4)$, $S(0,-2)$, $T(2,2)$, $U(2,1)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, if a point has coordinates $(x,y)$, its image has coordinates $(kx,ky)$. Here $k = 3$.
For point $R(0,-4)$: $R'(3\times0,3\times(-4))=(0,-12)$.
For point $S(0,-2)$: $S'(3\times0,3\times(-2))=(0,-6)$.
For point $T(2,2)$: $T'(3\times2,3\times2)=(6,6)$.
For point $U(2,1)$: $U'(3\times2,3\times1)=(6,3)$.

Answer:

$R'(0,-12)$
$S'(0,-6)$
$T'(6,6)$
$U'(6,3)$