World Science Scholars
19.3 Rotated Coordinate Systems in Two Dimensions

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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