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COMEDK · Maths · 10. Straight Lines

A line L passes through the point of intersection of the lines \(3x + y - 10 = 0\) and \(x - y - 2 = 0\). If the perpendicular distance of the line L from the point \((5, 1)\) is exactly \(\dfrac{2}{\sqrt{5}}\) units, which of the following represents the correct equation for line L?

  1. A \(x - 2y + 1 = 0\)
  2. B \(x + 2y - 5 = 0\)
  3. C \(2x + y - 7 = 0\)
  4. D \(2x - y - 5 = 0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x + 2y - 5 = 0\)

Step-by-step Solution

Detailed explanation

The point of intersection of the lines \(3x + y - 10 = 0\) and \(x - y - 2 = 0\) is obtained by solving the two equations. Adding the equations gives \(4x - 12 = 0 \Rightarrow x = 3\). Substituting \(x = 3\) into \(x - y - 2 = 0\) gives \(y = 1\). Thus, the point of intersection…