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 ze

Question

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 ze

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.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

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.

5 views Answered 2023-02-05 15:29