MHT CET · Maths · Straight Lines
The line through the points \((1,4),(-5,1)\) intersects the line \(4 x+3 y-5=0\) in the point
- A \((-1,-3)\)
- B \(\left(\frac{5}{3}, \frac{-5}{3}\right)\)
- C \((-1,3)\)
- D \((2,1)\)
Answer & Solution
Correct Answer
(C) \((-1,3)\)
Step-by-step Solution
Detailed explanation
Equation of line passing through \(\mathrm{A}(\mathrm{x}, \mathrm{y})=(1,4)\) and \(\mathrm{B}\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=(-5,1)\) is
\(\begin{array}{l}
\frac{y-4}{4-1}=\frac{x-1}{1+5} \\
\frac{y-4}{3}=\frac{x-1}{6} \Rightarrow 2(y-4)=x-1 \Rightarrow x-1-2 y+8=0 \\
x-2 y+7=0 ...(1)
\end{array}\)
Also given equation of line is \(4 x+3 y-5=0\) ...(2)
Solving (1) \& (2) we get \(x=-1, y=3\)
\(\begin{array}{l}
\frac{y-4}{4-1}=\frac{x-1}{1+5} \\
\frac{y-4}{3}=\frac{x-1}{6} \Rightarrow 2(y-4)=x-1 \Rightarrow x-1-2 y+8=0 \\
x-2 y+7=0 ...(1)
\end{array}\)
Also given equation of line is \(4 x+3 y-5=0\) ...(2)
Solving (1) \& (2) we get \(x=-1, y=3\)
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