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)

$(1, 1)$

Answer 2

The correct answer 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 $(1,1)$

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 $(1, 1)$,