Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original coordinates

From the graph, the coordinates of point $F$ are $(- 4,5)$, of point $G$ are $(4,5)$ and of point $H$ are $(-4,-4)$.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(kx,ky)$. Here $k = 2$.
For point $F(-4,5)$:
$x'=2\times(-4)=-8$, $y'=2\times5 = 10$. So the new coordinates of $F$ are $(-8,10)$.
For point $G(4,5)$:
$x'=2\times4 = 8$, $y'=2\times5=10$. So the new coordinates of $G$ are $(8,10)$.
For point $H(-4,-4)$:
$x'=2\times(-4)=-8$, $y'=2\times(-4)=-8$. So the new coordinates of $H$ are $(-8,-8)$.

Answer:

The coordinates of $F$ after dilation are $(-8,10)$, the coordinates of $G$ after dilation are $(8,10)$ and the coordinates of $H$ after dilation are $(-8,-8)$.