AP EAMCET · Maths · Straight Lines
A line passing through the point \(P(1,1)\) and parallel to the line \(x-y=5\) cuts the line \(x+3 y-2=0\) at \(Q\). Then twice the length of the segment \(P Q\) is
- A \(\sqrt{2}-1\)
- B \(2 \sqrt{3}-1\)
- C \(\sqrt{2}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
Equation of line through \(P(1,1)\) parallel to \(x-y=5\): \(x-y = 1-1 \implies x-y=0\) Intersection point \(Q\) of \(x-y=0\) and \(x+3y-2=0\): \(x=y \implies y+3y-2=0 \implies 4y=2 \implies y=\frac{1}{2}\) \(x=\frac{1}{2}\) \(Q = \left(\frac{1}{2}, \frac{1}{2}\right)\) Length…
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