1. **State the problem:** We have a triangle with vertices at points $(3, 2)$, $(7, 2)$, and $(3, 6)$. We want to reflect this triangle over the $y$-axis and find the new coordinates of the vertices. 2. **Formula for reflection over the $y$-axis:** When a point $(x, y)$ is reflected over the $y$-axis, its $x$-coordinate changes sign, while the $y$-coordinate remains the same. Mathematically, the reflection of $(x, y)$ over the $y$-axis is $(-x, y)$. 3. **Apply the reflection to each vertex:** - Reflect $(3, 2)$: $(-3, 2)$ - Reflect $(7, 2)$: $(-7, 2)$ - Reflect $(3, 6)$: $(-3, 6)$ 4. **Final answer:** The new coordinates of the triangle after reflection over the $y$-axis are $(-3, 2)$, $(-7, 2)$, and $(-3, 6)$.