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 one of the vertices of this rhombus is

Step-by-step solution

Given equation of lines of two sides of rhombus are x-y+1=0 & 7 x-y-5=0 On solving these two equation, we get (x, y)=(1,2)= point of intersection of two sides. So equation of diagonal passing through (1,2) and (-1,-2) y-2 y+2 = x-1 1-(-1) y=2 x is one diagonal so equation of other diagonal y=- 1 2 x+c -2=- 1 2 (-1)+ C C =- 5 2 equation of other diagonal is 2 y + x +5=0 ... (i) So solving given equation with equation (i) we get ( 1 3 ,- 8 3 )