By using the concept of slope,prove that diagonals of a rhombus are at right angles.

Let OABC be a rhombus having each side of a unit and height as b unit where O is the origin OA is along X-axis. Also, let BL and CM be perpendiculars drawn from the vertices B and C respectively to X-axis.

OM = c   (Say)

In DOMC and DALB, we have

OC = AB  (sides of rhombus)

CM = BL  (perpendicular drawn between same parallels)

ÐOMC = ÐALB = 90°

Thus, by RHS congruence criterion, we have DOMC @ DALB.

OM = AL

Þ AL = c

Therefore,

OM = c, CM = b, OA = a, OL = a + c and LB = b

Hence, the coordinates of the vertices are:

O(0, 0) A(a, 0), B(a + c, b) and C(c, b)

On applying Pythagoras theorem in right triangle OMC, we have

Hence the diagonal OB is perpendicular to diagonal AC.