How to rotate any geometric figure around a point that is not the origin
In short: Rotating shapes around the origin is straightforward, but shifting that center of rotation requires a specific three-step algebraic process. This video explains how to manipulate coordinates to perform rotations around any point on the plane.
To rotate a figure around a point other than the origin, you must first translate the entire plane so that your chosen center of rotation sits at the origin (0,0). Once the center is aligned, you apply the standard rotation rules for the origin. Finally, you translate the plane back to its original position to complete the transformation.
This method allows for precise algebraic coordinate notation when working with geometric figures that do not pivot around the standard coordinate center.
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Sources
- Summary by Intellect · source: Rotating algebraically about a point | Geometry (TX TEKS) | Khan Academy
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