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

Explanation:

Step1: Identify original coordinates

$E(-6, -4)$, $F(-2, -4)$, $G(-2, 3)$, $H(-6, 3)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula is $(x,y)\to(kx,ky)$. Here $k = 2$. For point $E$: $x=-6,y = - 4$, new coordinates $E'=(2\times(-6),2\times(-4))=(-12,-8)$ For point $F$: $x=-2,y=-4$, new coordinates $F'=(2\times(-2),2\times(-4))=(-4,-8)$ For point $G$: $x=-2,y = 3$, new coordinates $G'=(2\times(-2),2\times3)=(-4,6)$ For point $H$: $x=-6,y = 3$, new coordinates $H'=(2\times(-6),2\times3)=(-12,6)$

Answer:

$E'(-12,-8)$ $F'(-4,-8)$ $G'(-4,6)$ $H'(-12,6)$