Subjects geometry

Rotation 90Ccw

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1. **Problem Statement:** We need to find the image of square JKLM after a 90° counterclockwise rotation around the origin. 2. **Vertices of the original square JKLM:** - J(-8, 2) - K(-4, 2) - L(-4, 6) - M(-8, 6) 3. **Rotation formula for 90° counterclockwise around the origin:** $$ (x, y) \to (-y, x) $$ This means each point's new coordinates are found by swapping the x and y values and changing the sign of the original y-coordinate. 4. **Apply the rotation to each vertex:** - J(-8, 2) \to J'(-2, -8) - K(-4, 2) \to K'(-2, -4) - L(-4, 6) \to L'(-6, -4) - M(-8, 6) \to M'(-6, -8) 5. **Result:** The image of square JKLM after the rotation has vertices: - J'(-2, -8) - K'(-2, -4) - L'(-6, -4) - M'(-6, -8) This completes the rotation and gives the new position of the square on the coordinate plane.