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AP EAMCET · Maths · Straight Lines

If a straight line through the point \(P(1,2)\), which makes an angle \(45^{\circ}\) with the \(X\)-axis, meets the line \(3 x+4 y+5=0\) at \(Q\), then length of \(P Q\) equals ......... units

  1. A \(\frac{16 \sqrt{2}}{7}\)
  2. B \(\frac{\sqrt{7}}{2}\)
  3. C \(\frac{7 \sqrt{2}}{16}\)
  4. D \(\frac{16}{7}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{16 \sqrt{2}}{7}\)

Step-by-step Solution

Detailed explanation

Equation of line passing through the point \(P(1,2)\) which makes an angle \(45^{\circ}\) with the \(X\)-axis is \[ \begin{aligned} (y-2)=m(x-1) \text { and } m & =\tan \theta \\ & =\tan 45^{\circ}=1 \end{aligned} \] \(\therefore\) Equation is \(y-2=1(x-1)\)…