This demonstration shows how the distance between any given point and the origin stays the same even 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 calculates the distance between the point and the origin in both coordinate systems. Notice that the point itself stays fixed; only the coordinate labels of the point vary as the coordinate system is changed.