This interactive demonstration shows how coordinate labels of points change when the reference frame is rotated. Use the first two sliders to choose the $(x,y)$ coordinates of a point (represented by a white dot). Then use the third slider to choose the angle at which a second coordinate system—with coordinates $(x^\prime,y^\prime)$—is rotated relative to the first one. The demonstration calculates the coordinates of the chosen point in the new coordinate system. Notice that the point itself stays fixed; only the coordinate labels of the point vary as the coordinate system is changed.
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