Problem: Graph the image of ∆FGH after a dilation with a scale factor of 2 centered at the origin. 1. Formula: For a dilation centered at the origin with scale factor $k$, each point $(x,y)$ maps to $(kx,ky)$. 2. Given vertices: $F(-4,4)$, $G(0,4)$, $H(-2,-6)$. 3. Dilation mapping: $$ (x,y) \mapsto (2x,2y) $$ 4. Compute images: F: $F(-4,4) \to F'(-8,8)$ since $(-8,8) = (2\cdot -4, 2\cdot 4)$. G: $G(0,4) \to G'(0,8)$ since $(0,8) = (2\cdot 0, 2\cdot 4)$. H: $H(-2,-6) \to H'(-4,-12)$ since $(-4,-12) = (2\cdot -2, 2\cdot -6)$. 5. Final answer: The image vertices are $F'(-8,8)$, $G'(0,8)$, $H'(-4,-12)$. To graph the image, plot these points and connect them in the same order to form the dilated triangle; the origin remains fixed under the dilation.