KCET · Maths · Straight Lines
The foot of the perpendicular from the point \((2,4)\) upon \(x+y=4\) is
- A \((2,2)\)
- B \((4,0)\)
- C \((1,3)\)
- D \((3,-1)\)
Answer & Solution
Correct Answer
(C) \((1,3)\)
Step-by-step Solution
Detailed explanation
The equation of line perpendicular to \(x+y=4\) is \(\mathrm{y}-\mathrm{x}=\lambda\).
Also, it passes through \((2,4)\).
\[
\begin{array}{lr}
\therefore & 4-2=\lambda \\
\Rightarrow & \lambda=2 \\
\therefore & \text { Perpendicular line is } \\
& y-x=2
\end{array}
\]
The point of intersection of these lines are \((1,3)\).
Also, it passes through \((2,4)\).
\[
\begin{array}{lr}
\therefore & 4-2=\lambda \\
\Rightarrow & \lambda=2 \\
\therefore & \text { Perpendicular line is } \\
& y-x=2
\end{array}
\]
The point of intersection of these lines are \((1,3)\).
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