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 \[\] [Hint: Let the slope of the line be $m$. Then the equation of the line passing
through the fixed point $P (x_1
)$ is $y - y_1 = m (x - x_1
)$. Taking the algebraic sum
of perpendicular distances equal to zero, we get $ y - 1 = m (x - 1). $ Thus $(x_1
) $ is $(1, 1)$.]