41. This is a kite quadrilateral, whose<span> four sides can be grouped into two pairs of equal-length sides that are adjacent to each other, because FI=NI, FE=NE, as you can calculate from the given coordinates. However, this is not a rhombus, because the four side lengths are not all equal.
44. The rhombus is centered at (0,0). The two diagonals are evenly divided by the center. SO=OL=SL/2=2a/2=a. S(-a,0), L(a,0). FO=PO=FP/2=4b/2=2b. F(0,2b), P(0,-2b).
45. </span>P(a-b, c).<span>The y coordinate of P is the same as the y coordinate of (-b,c), which is c, because the two points are on the same horizontal line. The x coordinate of P - the x coordinate of (0,0) is the same as the x coordinate of (-b,c) - the x coordinate of (-a,0). So x=-b-(-a)=a-b. P(a-b, c).
46. Suppose the four coordinates of the kite are A(x,y), C(x+2a,y), B(x+a, y+b), D(x+a, y-b). The midpoint of AB is (x+a/2, y+b/2). midBC is (x+3a/2, y+b/2). midCD is (x+3a/2, y-b/2), midAD is (x+a/2. y-b/2). ABCD is a rectangle.</span>
