Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of point $D$ are $(- 2,-1)$, of point $E$ are $(2,-1)$ and of point $F$ are $(-2,1)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 4$, if a point has coordinates $(x,y)$, its new coordinates $(x',y')$ after dilation are given by $(x',y')=(k\cdot x,k\cdot y)$.
For point $D(-2,-1)$:
$x'_D=4\times(-2)=-8$, $y'_D = 4\times(-1)=-4$. So the new coordinates of $D$ are $(-8,-4)$.
For point $E(2,-1)$:
$x'_E=4\times2 = 8$, $y'_E=4\times(-1)=-4$. So the new coordinates of $E$ are $(8,-4)$.
For point $F(-2,1)$:
$x'_F=4\times(-2)=-8$, $y'_F=4\times1 = 4$. So the new coordinates of $F$ are $(-8,4)$.

Answer:

The coordinates of $D$ after dilation are $(-8,-4)$, the coordinates of $E$ after dilation are $(8,-4)$ and the coordinates of $F$ after dilation are $(-8,4)$.