Subjects geometry

Translation Reflection 11582E

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1. The problem asks to find the coordinate notation that represents a translation up 1 unit followed by a reflection over the x-axis. 2. Translation up 1 unit means adding 1 to the y-coordinate: $ (x, y) \to (x, y + 1) $. 3. Reflection over the x-axis means changing the sign of the y-coordinate: $ (x, y) \to (x, -y) $. 4. When combining transformations, apply them in order: first translate, then reflect. 5. Start with $ (x, y) $. 6. Translate up 1 unit: $ (x, y) \to (x, y + 1) $. 7. Reflect over the x-axis: $ (x, y + 1) \to (x, -(y + 1)) = (x, -y - 1) $. 8. Therefore, the combined transformation is $ (x, y) \to (x, -y - 1) $. 9. Among the options, this matches $ (x, y) \to (x, -y - 1) $. Final answer: $ (x, y) \to (x, -y - 1) $.