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

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

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Solution:

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