If the algebraic sum of perpendiculars from n given points on a variable straight line is zero then prove that the variable straight line passes through a fixed point

If the algebraic sum of the perpendiculars from the points (2,0),(0,2),(1,1) to a variable line be zero, then prove that line passes through a fixed-point whose coordinates are (1,1)dot

Let the algebraic sum of the perpendicular distance from the points (2, 0), (0,2), and (1, 1) to a variable straight line be zero. Then the line passes through a fixed point whose coordinates are___

Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

Which one of the following curves is the orthogonal trajectory of straight lines passing through a fixed point (a,b) ?

If the algebraic sum of the distances of a variable line from the points (2,0),(0,2), and (-2,-2) is zero, then the line passes through the fixed point. (a) (-1,-1) (b) (0,0) (c) (1,1) (d) (2,2)

The algebraic sum of the perpendicular distances from A(x_1, y_1) , B(x_2, y_2) and C(x_3, y_3) to a variable line is zero. Then the line passes through (A) the orthocentre of triangleABC (B) centroid of triangleABC (C) incentre of triangleABC (D) circumcentre of triangleABC

A straight line moves such that the algebraic sum of the perpendiculars drawn to it from two fixed points is equal to 2k . Then, then straight line always touches a fixed circle of radius. 2k (b) k/2 (c) k (d) none of these

From a variable point on the tangent at the vertex of a parabola y^2=4a x , a perpendicular is drawn to its chord of contact. Show that these variable perpendicular lines pass through a fixed point on the axis of the parabola.

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2,0), (0,2) and (1,1) on the line is zero. Find the coordinate of the point P.