Question

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

Answer 1

`y = sqrt{a^2 - b^2}`

Explanation:

`|AB|^2 = b^2 + y^2`

`|BC|^2 = a^2`

`|CD|^2 = b^2 + y^2`

`|DA|^2 = a^2 = b^2 + y^2`