1. **Problem:** Translate rectangle QRST with vertices Q(-6, -1), R(-3, 1), S(1, -5), and T(-2, -7) by the rule $(x, y) \to (x + 5, y + 7)$. 2. **Formula:** To translate a point $(x, y)$ by $(h, k)$, use: $$ (x, y) \to (x + h, y + k) $$ where $h$ is the horizontal shift and $k$ is the vertical shift. 3. **Apply translation to each vertex:** - For $Q(-6, -1)$: $$ Q' = (-6 + 5, -1 + 7) = (-1, 6) $$ - For $R(-3, 1)$: $$ R' = (-3 + 5, 1 + 7) = (2, 8) $$ - For $S(1, -5)$: $$ S' = (1 + 5, -5 + 7) = (6, 2) $$ - For $T(-2, -7)$: $$ T' = (-2 + 5, -7 + 7) = (3, 0) $$ 4. **Final answer:** - $Q'(-1, 6)$ - $R'(2, 8)$ - $S'(6, 2)$ - $T'(3, 0)$ Each vertex is shifted 5 units right and 7 units up, preserving the shape and size of the rectangle.