Question

The algebraic sum of the perpendicular distances from A(x1y1), B(x2,y2) and C(x3y3) to a variable line is zero, then the line passes through:

Solution

Correct option is

The centroid Δ ABC

Let Ax + By + C = 0 be the equation of line.

  

   

  

                                           [where (xgyg) ≡ centroid of Δ ABC]

Hence, line passes through the centroid of triangle.

SIMILAR QUESTIONS

Q1

Given the triangle A (10, 4), B(–4, 9), C(–2, 1), find the equation of median through B.

Q2

Find the equation of the straight line passing through the points (3, 3) and (7, 6). What is the length of the portion of the line intercepted between the axes of the coordinates.

Q3

Given the triangle with vertices A (–4, 9), B (10, 4), C (–2, –1). Find the equation of the altitude through A.

Q4

Find the equation of perpendicular bisector of the line joining the points (1, 1) and (2, 3). 

Q5

Find the coordinates of the foot of the perpendicular from the point (2, 3) on the line y = 3x + 4.

Q6

Find the equation of the line passing through (ab) and parallel to px +qy + 1 = 0.  

Q7

Find the equation of the line perpendicular to 3x + 4y + 1= 0 and passing through (1, 1).

Q8

Find the distance of line h (x + h) + k (y + k) = 0 from the origin.

Q9

Determine the distance between the lines : 6x + 8y – 45 = 0 and 3x + 4y – 5 = 0.

Q10

If A (cos α, sin α), B (sin α, –cos α), C (1, 2) are the vertices of a ΔABC, then as α varies the locus of its centroid is: