1. **Problem statement:** We have a triangle with vertices at approximately (2,3), (5,3), and (5,7). The triangle is reflected across a vertical line, and two vertices of the reflected triangle are given as (7,3) and (7,7). We need to find the coordinates of the third vertex of the reflected triangle. 2. **Understanding reflection across a vertical line:** When a point $(x,y)$ is reflected across a vertical line $x = k$, the reflected point $(x', y')$ has the same $y$-coordinate, and the $x$-coordinate satisfies: $$x' = 2k - x$$ 3. **Identify the original points and their reflections:** - Original vertices: $(2,3)$, $(5,3)$, $(5,7)$ - Reflected vertices given: $(7,3)$ and $(7,7)$ 4. **Find the line of reflection $x = k$ using the known points:** - The point $(5,3)$ reflects to $(7,3)$, so: $$7 = 2k - 5 \implies 2k = 12 \implies k = 6$$ - Check with $(5,7)$ reflecting to $(7,7)$: $$7 = 2k - 5 \implies k = 6$$ So the line of reflection is $x=6$. 5. **Find the reflection of the remaining vertex $(2,3)$:** $$x' = 2 \times 6 - 2 = 12 - 2 = 10$$ $$y' = 3$$ 6. **Answer:** The other vertex of the reflected triangle is at $(10,3)$.