1. **Problem Statement:** We are given a triangle PQR with vertices at points $P(3,6)$, $Q(4,8)$, and $R(2,9)$. We need to find the coordinates of the triangle after translating it 7 units to the left. 2. **Translation Rule:** When translating a point horizontally, subtract the translation distance from the x-coordinate. The y-coordinate remains unchanged. 3. **Apply Translation:** - For point $P(3,6)$, new coordinates are $P' = (3 - 7, 6) = (-4, 6)$. - For point $Q(4,8)$, new coordinates are $Q' = (4 - 7, 8) = (-3, 8)$. - For point $R(2,9)$, new coordinates are $R' = (2 - 7, 9) = (-5, 9)$. 4. **Result:** The translated triangle $P'Q'R'$ has vertices at $P'(-4,6)$, $Q'(-3,8)$, and $R'(-5,9)$. This translation shifts the entire triangle 7 units left without changing its shape or orientation.