1. **Problem statement:** We have a pentagon DEFGH with a vertical line of symmetry at $x=7$. Points E, F, and G have coordinates $E(7,10)$, $F(11,8)$, and $G(12,0)$. We need to find the coordinates of points D and H, which lie on the left side of the pentagon. 2. **Understanding symmetry:** A vertical line of symmetry at $x=7$ means that for any point on the right side, its symmetric point on the left side has the same $y$-coordinate but the $x$-coordinate is reflected across $x=7$. 3. **Formula for reflection:** If a point $(x,y)$ is reflected across the vertical line $x=a$, its image is $(2a - x, y)$. 4. **Find D:** Point F is at $(11,8)$ on the right side. Its symmetric point D on the left side will have coordinates: $$D_x = 2 \times 7 - 11 = 14 - 11 = 3$$ $$D_y = 8$$ So, $D = (3,8)$. 5. **Find H:** Point G is at $(12,0)$ on the right side. Its symmetric point H on the left side will have coordinates: $$H_x = 2 \times 7 - 12 = 14 - 12 = 2$$ $$H_y = 0$$ So, $H = (2,0)$. **Final answer:** $$D = (3,8), \quad H = (2,0)$$