![\[\begin{array}{*{35}{l}} \Rightarrow ~2a\text{ }-\text{ }1\text{ }+\text{ }2b\text{ }-\text{ }1\text{ }+\text{ }a\text{ }+\text{ }b\text{ }-\text{ }1\text{ }=\text{ }0 \\ \Rightarrow ~3a\text{ }+\text{ }3b\text{ }-\text{ }3\text{ }=\text{ }0 \\ \Rightarrow ~a\text{ }+\text{ }b\text{ }-\text{ }1\text{ }=\text{ }0 \\ \Rightarrow ~a\text{ }+\text{ }b\text{ }=\text{ }1 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-939d77e22b3465b4c24d46fb313ccc63_l3.png "Rendered by QuickLaTeX.com")
So, the equation ax + by = 1 represents a family of straight lines passing through a fixed point.
Comparing the equation ax + by = 1 and a + b = 1, we get
x = 1 and y = 1
So, the coordinates of fixed point is (1, 1)
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 coordinates of the point 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 coordinates of the point P.