Question

The coordinates of the vertices of a parallelogram ABCD are A(O,O), B(b,y), C(a+b,y), D(a,0). If ABCD is a rhombus, express y in terms of a and b?

Answer 1

Assume \(a,b>0\). Since ABCD is a rhombus, the lines containing A and C, and B and D (respectively), are perpendicular. (i.e. AC is perpendicular to BD).