The rectangle with vertices (0,0), (0,3), (2,0) and (2,3) is rotated clockwise through a right angle about the point (2,0), then about (5,0), then about (7,0), and finally about (10,0). The net effect is to translate it a distance 10 along the x-axis. The point initially at (1,1) traces out a curve. Find the area under this curve (in other words, the area of the region bounded by the curve, the x-axis and the lines parallel to the y-axis through (1,0) and (11,0)).
geometryintegrationcalculusgeometric transformationrotation