Hello, mathdonkey
If you think that this is a difficult problem, you ain't seen nothing yet!
Prove that quadrilateral: W(½, 1½), X(4, 1), Y(3½, 5½), Z(1, 6) is a rhombus. It's always a good idea to make a sketch . . .
Code:
Z 
*  Y
(1,6)  *
 (3½,5½)



W 
*  X
(½,1½) *
 (4,1)
    +          

Do you know what makes a quadrilateral a rhombus?
. . That's right . . . it has four equal sides.
Does WXYZ has four equal sides?
. . How can we determine if: .$\displaystyle WX \:=\: XY\:=\:YZ \:=\:ZW$ ?
That's right . . . the Distance Formula.
Go for it!