To solve this problem, we need to apply a dilation with a scale factor of 2, centered at the origin, to the vertices of triangle $\Delta FGH$.

1. Original coordinates:

   • $F(-4, 4)$
   • $G(4, 4)$
   • $H(0, -4)$

2. Dilating each point by a factor of 2: For dilation centered at the origin, each coordinate of a point is multiplied by the scale factor.

   • $F' = (-4 \times 2, 4 \times 2) = (-8, 8)$
   • $G' = (4 \times 2, 4 \times 2) = (8, 8)$
   • $H' = (0 \times 2, -4 \times 2) = (0, -8)$

3. New coordinates after dilation:

   • $F'(-8, 8)$
   • $G'(8, 8)$
   • $H'(0, -8)$

To graph the dilated triangle, you would plot the new points $F'(-8, 8)$, $G'(8, 8)$, and $H'(0, -8)$ on the graph and connect them to form the new image of triangle $\Delta FGH$.

Would you like further details or assistance in graphing this?

Here are 5 related questions:

1. How do you determine the center of dilation in any transformation?
2. What happens to the size of a shape after a dilation with a scale factor greater than 1?
3. How do you apply a dilation to shapes not centered at the origin?
4. Can you describe the difference between dilation and translation?
5. How would a dilation with a fractional scale factor affect the triangle?

Tip: When performing dilations, always multiply both the x- and y-coordinates of each point by the scale factor to get the image coordinates.