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

The correct option is C $(1,1)$

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.