Two of the edges of a rectangular part are represented by two lines in the x-y plane on a CMM worktable, as illustrated in. It is desired to mathematically redefine the coordinate system so that the two edges are used as the x- and y-axes, rather than the regular x-y axes of the CMM. To define the new coordinate system, two parameters must be determined: (a) the origin of the new coordinate system must be located in the existing CMM axis system; and (b) the angle of the x-axis of the new coordinate system must be determined relative to the CMM x-axis. Two points on the first edge (line 1) have been measured by the CMM and the coordinates are (46.21, 22.98) and (90.25, 32.50), where the units are mm. Also, two points on the second edge (line 2) have been measured by the CMM and the coordinates are (26.53, 40.75) and (15.64, 91.12). The coordinates have been corrected for the radius of the probe. Find (a) the coordinates of the new origin relative to the CMM origin and (b) degrees of rotation of the new x-axis relative to the CMM x-axis. (c) Are the two lines (part edges) perpendicular?