MHT CET · Maths · Straight Lines
The co-ordinates of the foot of the perpendicular from the point \((1,2)\) on the line \(x-3 y+7=0\) are
- A \(\left(\frac{4}{5}, \frac{13}{5}\right)\)
- B \((-13,-2)\)
- C \(\left(\frac{-13}{5}, \frac{-2}{5}\right)\)
- D \((2,3)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{4}{5}, \frac{13}{5}\right)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{x-1}{1}=\frac{y-2}{-3}=\frac{-(1-3 \times 2+7)}{1^2+(-3)^2} \\ & \Rightarrow \frac{x-1}{1}=\frac{y-2}{-3}=\frac{-2}{10} \\ & \Rightarrow x=\frac{4}{5} \text { and } y=\frac{13}{5} \\ & \Rightarrow\left(\frac{4}{5}, \frac{13}{5}\right)\end{aligned}\)
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