Four students are trying to find the rule that translates point \( N(-2,-4) \) to \( N^{\prime}(2,4) \). Each student's reasoning is shown below. \( \begin{array}{ll}\text { Raheem: } & \text { The rule is }(x \bullet(-1), y \bullet(-1)) \text { because }-2 \bullet(-1)=2 \text { and }-4 \bullet(-1)=4 \\ \text { Casey: } & \text { The rule is }(x+2, y+4) \text { because the image is }(2,4) \text {. } \\ \text { Andrew: } & \text { The rule is }(x+4, y+0) \text { because the coordinates are opposites. } \\ \text { Lo: } & \text { The rule is }(x+4, y+8) \text { because }-2+4=2 \text { and }-4+8=4 . \\ \text { Which student is correct? } \\ \text { Raheem } \\ \text { Casey } \\ \text { Andrew } \\ \text { Lo }\end{array} \)

To determine which student correctly identifies the rule that translates point \( N(-2, -4) \) to \( N^{\prime}(2, 4) \), let's evaluate each proposed rule: 1. **Raheem:** **Rule:** \( (x \times (-1), y \times (-1)) \) **Application:** \[ (-2 \times (-1), -4 \times (-1)) = (2, 4) \] **Analysis:** This correctly maps \( N \) to \( N^{\prime} \). However, this operation is a reflection through the origin, not a translation. 2. **Casey:** **Rule:** \( (x + 2, y + 4) \) **Application:** \[ (-2 + 2, -4 + 4) = (0, 0) \] **Analysis:** This maps \( N \) to \( (0, 0) \), which is incorrect. 3. **Andrew:** **Rule:** \( (x + 4, y + 0) \) **Application:** \[ (-2 + 4, -4 + 0) = (2, -4) \] **Analysis:** This maps \( N \) to \( (2, -4) \), which is incorrect. 4. **Lo:** **Rule:** \( (x + 4, y + 8) \) **Application:** \[ (-2 + 4, -4 + 8) = (2, 4) \] **Analysis:** This correctly maps \( N \) to \( N^{\prime}(2, 4) \). **Conclusion:** While Raheem's rule mathematically maps \( N \) to \( N^{\prime} \), it describes a reflection rather than a translation. Lo's rule correctly describes a translation that shifts \( N \) to \( N^{\prime} \). **Answer:** Lo