Two sides of a rhombus are along the lines, x - y + 1 = 0 and 7 x - y - 5 = 0 . If its diagonals intersect at - 1 , - 2 , then which one of the following is a vertex of this rhombus ?

Step-by-step solution

d 1   : y - 2 = - 2 - 2 - 1 - 1   x - 1 y - 2 = 2 x - 1 y - 2 x = 0 d 2 ⊥ d 1   ⇒       2 y + x = k  , - 1 ,   - 2 Lies on it ∴ k = -5 ⇒ 2 y + x + 5 = 0 Now point of intersection of d 2 and L 1 x - y + 1 = 0     . . . . . . 1 x + 2 y + 5 = 0       . . . . . . . 2 on solving 1   &   2 - 3 y - 4 = 0 y =   - 4 3 And point of intersection of d 2 and L 2 x + 2 y + 5 = 0       . . . . . . 3 14 x - 2