graph the image of △fgh after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify the coordinates of vertices

Let's assume $F(-4,4)$, $G(0,4)$, $H(-2, - 5)$.

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor $k = 2$, the formula to find the coordinates of the dilated point $(x',y')$ from the original point $(x,y)$ is $(x',y')=(kx,ky)$. For point $F(-4,4)$: $x_F'=2\times(-4)=-8$, $y_F'=2\times4 = 8$, so $F'(-8,8)$. For point $G(0,4)$: $x_G'=2\times0 = 0$, $y_G'=2\times4=8$, so $G'(0,8)$. For point $H(-2,-5)$: $x_H'=2\times(-2)=-4$, $y_H'=2\times(-5)=-10$, so $H'(-4,-10)$.

Step3: Graph the new triangle

Plot the points $F'(-8,8)$, $G'(0,8)$ and $H'(-4,-10)$ on the coordinate - plane and connect them to form $\triangle F'G'H'$.

Answer:

Graph $\triangle F'G'H'$ with vertices $F'(-8,8)$, $G'(0,8)$ and $H'(-4,-10)$.