Diagonals of a rhombus bisect each other perpendicularly. Thus, O is the mid point of QS and RP. Coordinates of midpoint of line joining A = (x1,y1) and B = (x2,y2) is (
x1+x2
2
,
y1+y2
2
) ⇒ O = (
3−7
2
,
1+5
2
)=(−2,3) Slope of PR =
1−5
3+7
=−
2
5
Product of slopes of two perpendicular lines is -1 ⇒ Slope of QS = m×−
2
5
=−1 ⇒ m=
5
2
∴ Equation oof line QS with slope m=
5
2
and passing through point O (x1,y1)=(−2,3) =(y−y1)=m(x−x1) =(y−3)=