Subjects geometry

Rotated Coordinates 3C0B05

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1. The problem is to find the final coordinates of a point after rotation on a graph. 2. The formula for rotating a point $(x,y)$ by an angle $\theta$ counterclockwise about the origin is: $$x' = x\cos\theta - y\sin\theta$$ $$y' = x\sin\theta + y\cos\theta$$ 3. Important rules: - The angle $\theta$ is measured in radians. - Rotation preserves the distance from the origin. 4. Suppose the original point is $(x,y)$ and the rotation angle is $\theta$. 5. Substitute the values of $x$, $y$, and $\theta$ into the formulas. 6. Calculate $x'$ and $y'$ step-by-step, showing intermediate simplifications. 7. The final coordinates after rotation are $(x', y')$. Since the user did not provide specific coordinates or angle, this is the general method to find the rotated coordinates.