Question: Reflect the figure over the line $x = -1$. Plot all of the points of the reflected figure. You may click a plotted point to delete it. Graph shape: a triangle in the bottom-right of the coordinate plane with vertices at $(1, -2)$, $(4, -3)$, and $(1, -8)$; reflect it across $x = -1$.
1. **State the problem:** We need to reflect a triangle with vertices at $ (1, -2)$, $ (4, -3)$, and $ (1, -8)$ across the vertical line $x = -1$.
2. **Reflection formula:** When reflecting a point $ (x, y)$ across the vertical line $x = a$, the reflected point $ (x', y')$ is given by:
$$x' = 2a - x, \quad y' = y$$
3. **Apply the formula to each vertex:**
- For $ (1, -2)$:
$$x' = 2(-1) - 1 = -2 - 1 = -3, \quad y' = -2$$
- For $ (4, -3)$:
$$x' = 2(-1) - 4 = -2 - 4 = -6, \quad y' = -3$$
- For $ (1, -8)$:
$$x' = 2(-1) - 1 = -3, \quad y' = -8$$
4. **Reflected vertices:** The reflected triangle has vertices at:
$$(-3, -2), (-6, -3), (-3, -8)$$
5. **Explanation:** Each point is mirrored across the line $x = -1$ by calculating the horizontal distance from the point to the line and placing the reflected point the same distance on the opposite side.
**Final answer:** The reflected triangle vertices are $(-3, -2)$, $(-6, -3)$, and $(-3, -8)$.