Question: Write the coordinates of the vertices after a dilation with a scale factor of $2$, centered at the origin.
$F(-4, 5)$, $G(4, 5)$, $H(-5, -4)$
After dilation by scale factor $2$ centered at the origin, the triangle’s vertices move to $F'(-8, 10)$, $G'(8, 10)$, $H'(-10, -8)$.
1. **State the problem:** We need to find the coordinates of the vertices of triangle $FGH$ after a dilation with scale factor $2$ centered at the origin.
2. **Recall the dilation formula:** For a point $(x, y)$, dilation centered at the origin with scale factor $k$ transforms it to $(kx, ky)$.
3. **Apply the formula to each vertex:**
- For $F(-4, 5)$: $$F' = (2 \times -4, 2 \times 5) = (-8, 10)$$
- For $G(4, 5)$: $$G' = (2 \times 4, 2 \times 5) = (8, 10)$$
- For $H(-5, -4)$: $$H' = (2 \times -5, 2 \times -4) = (-10, -8)$$
4. **Conclusion:** The vertices after dilation are $F'(-8, 10)$, $G'(8, 10)$, and $H'(-10, -8)$.
This completes the dilation process centered at the origin with scale factor $2$.