Subjects geometry

Triangle Rotation 900D00

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1. **Problem statement:** Triangle C is rotated 180° clockwise about the origin. We need to find the new location of Triangle C after this rotation. 2. **Rotation formula:** For a point $(x,y)$ rotated 180° clockwise about the origin, the new coordinates are given by: $$ (x', y') = (-x, -y) $$ This means each coordinate changes sign. 3. **Applying the rotation:** Since Triangle C is in quadrant IV (where $x > 0$ and $y < 0$), applying the rotation: $$ (x', y') = (-x, -y) $$ Since $x > 0$, $-x < 0$; since $y < 0$, $-y > 0$. 4. **Resulting quadrant:** The new coordinates $(x', y')$ have $x' < 0$ and $y' > 0$, which places the rotated triangle in quadrant II. 5. **Conclusion:** The triangle in quadrant II is Triangle A, so the new location of Triangle C after a 180° clockwise rotation about the origin is Triangle A. **Final answer:** Triangle C maps to Triangle A after the rotation.