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A variable line passes through a fixed p...

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.

Text Solution

Verified by Experts

Let the equation of the variable line be
ax+by+c = 0
Then according to the given condition, we get
`(2a+c)/(sqrt(a^(2) + b^(2))) + (2b+c)/(sqrt(a^(2) + b^(2))) + (-2a-2b+c)/(sqrt(a^(2)+b^(2))) = 0`
or c=0
which shows that the line passes through (0,0) for all values of a and b.
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