1. **Problem Statement:** We have a pentagon DEFGH symmetric about the vertical line $x=7$. Given points are $E(7,10)$, $F(11,8)$, and $G(12,0)$. We need to find coordinates of $D$ and $H$ which are symmetric to $F$ and $G$ respectively. 2. **Key Concept:** For a point $(x,y)$ reflected about the vertical line $x=a$, the reflected point is $(2a - x, y)$. 3. **Find D:** Point $D$ is symmetric to $F(11,8)$ about $x=7$. Calculate $x$-coordinate of $D$: $$x_D = 2 \times 7 - 11 = 14 - 11 = 3$$ The $y$-coordinate remains the same: $$y_D = 8$$ So, $D = (3,8)$. 4. **Find H:** Point $H$ is symmetric to $G(12,0)$ about $x=7$. Calculate $x$-coordinate of $H$: $$x_H = 2 \times 7 - 12 = 14 - 12 = 2$$ The $y$-coordinate remains the same: $$y_H = 0$$ So, $H = (2,0)$. **Final answer:** $$D = (3,8), \quad H = (2,0)$$