Let the coordinate A be (0,c) Equations of the given lines are x−y+2=0 and 7x−y+3=0 We know that the diagonals of the rhombus will be parallel to the angle bisectors of the two given lines; y=x+2 and y=7x+3 ∴ equation of angle bisectors is given as:
x−y+2
√2
=±
7x−y+3
5√2
5x−5y+10=±(7x−y+3) ∴ Parallel equations of the diagonals are 2x+4y−7=0 and 12x−6y+13=0 ∴ slopes of diagonals are
−1
2
and 2 . Now, slope of the diagonal from A(0,c) and passing through P(1,2) is (2−c) ∴2−c=2⇒c=0 (not possible) ∴2−c=