![]() We denote the rotated points by adding a prime (e.g., the rotation of E1 is E1', etc.). The entire figure is rotated by angle u, with center of rotation = O, so that the x-axis OE1 is rotated to a line through X = (-2,2). Suppose that on the plane, O, E1, and E2 and points P, P1, and P2 be as in Example 1, with coordinate axes OE1 and OE2. Given that the x-axis is rotated to the line OX, with X = (4,3), if P = (3.2), find the coordinates of all the labeled points in the figure We denote the rotated points by adding a prime (e.g., the rotation of E1 is E1', etc.) Now suppose that this entire figure is rotated by angle u, with center of rotation = O. ![]() The x-axis is the line OE1 and the y-axis is the line OE2. These figures may help you figure out or explain the formula. Check that this works even if Q is not in the first quadrant, for example, if Q1=(-3,2), what is Q1'?.If Q' is obtained by rotating Q by 90 degrees with center O = (0,0), what are the coordinates of Q? Then P' is obtained by rotating P by 90 degrees with center O = (0,0). ![]()
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