Subjects geometry

Reflection Coordinates A7700B

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1. **State the problem:** We need to find the coordinates of point Q(2, 3) after two reflections: first in the x-axis, then in the y-axis. 2. **Recall reflection rules:** - Reflection in the x-axis changes the y-coordinate sign: $ (x, y) \to (x, -y) $. - Reflection in the y-axis changes the x-coordinate sign: $ (x, y) \to (-x, y) $. 3. **Apply the first reflection (x-axis):** Starting with $Q = (2, 3)$, $$ Q' = (2, -3) $$ 4. **Apply the second reflection (y-axis) to $Q'$:** $$ Q'' = (-2, -3) $$ 5. **Interpretation:** After reflecting Q first in the x-axis and then in the y-axis, the point moves from $(2, 3)$ to $(-2, -3)$. This means both coordinates have changed sign. **Final answer:** The coordinates of Q after the two reflections are $\boxed{(-2, -3)}$.