This interactive demonstration illustrates the relationship between two coordinate systems that differ by a rotation about the origin followed by a translation in the $x$-direction. Use the first two sliders to choose the $(x,y)$ coordinates of a point (represented by a white dot). Then use the next two sliders to choose a second coordinate system—with coordinates $(x^\prime,y^\prime)$—that is rotated and translated 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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