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

$B(- 3,-2)$, $C(1,-2)$, $D(1,3)$, $E(-3,3)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 3$, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x',y')=(kx,ky)$.
For point $B(-3,-2)$:
$x'=3\times(-3)=-9$, $y'=3\times(-2)=-6$. So the new coordinates of $B$ are $(-9,-6)$.
For point $C(1,-2)$:
$x'=3\times1 = 3$, $y'=3\times(-2)=-6$. So the new coordinates of $C$ are $(3,-6)$.
For point $D(1,3)$:
$x'=3\times1 = 3$, $y'=3\times3 = 9$. So the new coordinates of $D$ are $(3,9)$.
For point $E(-3,3)$:
$x'=3\times(-3)=-9$, $y'=3\times3 = 9$. So the new coordinates of $E$ are $(-9,9)$.

Answer:

$B(-9,-6)$, $C(3,-6)$, $D(3,9)$, $E(-9,9)$