is a variable line such that the algebraic sum of the distances of the points, and from the line is equal to zero. The line will always pass-through
Explanation for the correct option:
Step:1 Finding condition of sum of distances of point is zero
Given the points are , and
Here is the mid point of
Then the distance form the point is same as the distance from to
Then the algebraic sum of the distance is zero.
Line is always passes through the point
Let be the equation of line, then we have,
Step:2 Finding slope of the line using algebric sum of distances is zero
The algebraic sum of the distance is zero.
Taking the denominator to RHS since the denominator is same.
Then we get,
Substituting in
Step:3 Finding equation of line and the point
The equation of line becomes
Therefore the line passes through the point
Hence, option (A) is the correct answer.