The coordinates of the foot of the perpendicu | vedclass

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(C) Let $P$ be the foot of the perpendicular from the origin $(0,0)$ to the line $x+y=2$.Since $P$ lies on a line perpendicular to $x+y=2$, its equati

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$(1,1)$

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(C) Let $P$ be the foot of the perpendicular from the origin $(0,0)$ to the line $x+y=2$.Since $P$ lies on a line perpendicular to $x+y=2$, its equation is of the form $x-y+k=0$.This line passes through the origin $(0,0)$, so $0-0+k=0$, which gives $k=0$.Thus, the equation of the line $OP$ is $y=x$.The coordinates of $P$ are obtained by solving the system of equations:$x+y=2$$y=x$Substituting $y=x$ into the first equation, we get $x+x=2$, which implies $2x=2$, so $x=1$.Since $y=x$, we have $y=1$.Therefore, the coordinates of the foot of the perpendicular $P$ are $(1,1)$.

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

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