A straight line moves in such a way that the algebraic sum of the perpendicular distance on it form the vertices of a given triangle is always zero. Show that the stright line always passes through the centroid of the triangle.

A straight line moves in such a manner that the sum of the reciprocals of its intercepts upon the axes is always constant. Show that the line passes throught a fixed point .

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

A point moves so that sum of the squares of its distances from the vertices of a triangle is always constant. Prove that the locus of the moving point is a circle whose centre is the centroid of the given triangle.

A straight line moves in such a maaner that the sum of the reciprocals of its intercepts upon the coordinate axes is always (1)/(2) . Show that line always passes through the point (2,2)

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___

Sum of the reciprocal intercepts on the axes by a moving straight line in its all position remain constant .Show that straight line always passes throguh a fixed point .

Find the locus of the foot of the perpendicular from the origin upon a stright line which always passes through the point (2,3).

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of a triangle ABC. lx+my+n=0 is an equation of the line L. Answer the following questions based on above passage : If the centroid of the triangle ABC is at the origin and algebraic sum of the length of the perpendiculars from the vertices of the triangle ABC on the line L is equal to 1 then sum of the squares of the intercepts made by L on the coordinate axes is equal to

A straight line is perpendicular to the straight line 3x-4y=6 and passes through (2,1) . Find its equation.