Translation Coordinates Fa6223

1. **State the problem:** We need to find the new coordinates of point $M(-1, 5)$ after applying the translation rule $(x, y) \to (x + 3, y - 2)$. 2. **Recall the translation formula:** A translation moves every point by adding a fixed amount to the $x$ and $y$ coordinates. Here, the translation adds $3$ to $x$ and subtracts $2$ from $y$. 3. **Apply the translation:** $$ (x, y) = (-1, 5) \to (x + 3, y - 2) = (-1 + 3, 5 - 2) $$ 4. **Simplify the coordinates:** $$ (-1 + 3, 5 - 2) = (2, 3) $$ 5. **Conclusion:** The image of point $M(-1, 5)$ after the translation is at coordinates $(2, 3)$. **Answer:** $(2, 3)$