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AP EAMCET · Maths · Straight Lines

If \(M\) is the foot of the perpendicular drawn from the origin to the line \(x-2 y+3=0\) which meets the \(X\) and \(Y\)-axes at \(A\) and \(B\) respectively, then \(A M=\)

  1. A \(\frac{6 \sqrt{10}}{5}\)
  2. B \(6 \sqrt{5}\)
  3. C \(\frac{6 \sqrt{5}}{5}\)
  4. D \(6 \sqrt{10}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{6 \sqrt{5}}{5}\)

Step-by-step Solution

Detailed explanation

\(A: y=0 \Rightarrow x=-3 \Rightarrow A=(-3,0)\) Line \(x-2y+3=0\). Perpendicular from origin \(O(0,0)\) is \(y=-2x\). Substitute \(y=-2x\) into line: \(x-2(-2x)+3=0 \Rightarrow 5x+3=0 \Rightarrow x=-\frac{3}{5}\).…