Subjects geometry

Gas Station Rotation 5A1D66

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1. **Problem Statement:** Rotate the Gas Station, a rectangle with vertices A, B, C, D, by 180 degrees about the origin. 2. **Formula for Rotation:** To rotate a point $(x,y)$ by 180 degrees about the origin, use the formula: $$ (x,y) \to (-x,-y) $$ This means each coordinate is negated. 3. **Apply the Rotation:** - If the original vertices of the Gas Station are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$, and $D(x_4,y_4)$, - Then the rotated vertices will be: $$ A' = (-x_1,-y_1), B' = (-x_2,-y_2), C' = (-x_3,-y_3), D' = (-x_4,-y_4) $$ 4. **Explanation:** Rotating 180 degrees flips the figure across the origin, moving each point to the opposite quadrant while preserving the shape and size. 5. **Final Answer:** The Gas Station's vertices after rotation are the negations of their original coordinates. Note: Without specific coordinates, the answer is expressed in terms of the original points' coordinates.