If the algebraic sum of the perpendicular distances from the points (2 ,0 ) , (0 ,2 ) and (1 ,1 ) to a variable line is zero, then the variable line always passes through a fixed point. The coordinat…

Question

If the algebraic sum of the perpendicular distances from the points (2 ,0 ) , (0 ,2 ) and (1 ,1 ) to a variable line is zero, then the variable line always passes through a fixed point. The coordinates of that point are

Accepted Answer

Correct answer: D. (d) Let a variable line is ax+ by+c=0…..(i) now, perpendicular distance from (2 ,0 ) , (0 ,2 ) and (1 ,1 ) to the line is respectively d_1= 2a+c a^2+b^2 , d_2= 2 b+c a^2+b^2 and_3= a+b+c a^2+b^2 Since, d_1+d_2+d_3=0 ⇒a+b+c=0 ⇒c=-a-b Now from equation (i) c=- ax ,- by ⇒ (x ,y )= (1 ,1 )

$If the algebraic sum of the perpendicular distances from the points (2, 0), (0, 2) and (1, 1) to a variable line is zero, then the variable line always passes through a fixed point. The coordinates of that point are$

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