Question

The coordinates of the foot of the perpendicular from $(0,0)$ upon the line $x+y=2$ are

• A. $(2,-1)$
• B. $(-2,1)$
• C. $(1,1)$
• D. $(1,2)$

Answer 1

Answer: (C)

Let $P$ be the foot of
perpendicular lies on line $x+y=2$

$\Delta OAB$ is an isosceles triangle,
Here, $P$ is the mid point of $AB$
$\therefore$ Coordinates of $P$ are $(1,1)$
Alternative Let the perpendicular line of $x+y=2$ is
$y-x=\lambda$
It passes through $(0,0)$, then $\lambda =0$
$\therefore y-x=0$
The point of intersection of $y-x=0$ and $x+y=2$ is $(1,1)$,
which is the required coordinates