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TS EAMCET · Maths · Straight Lines

If the line passing through the point \((4,-3)\) and having negative slope makes an angle of \(45^{\circ}\) with the line joining the points \((1,1),(2,3)\) then the sum of intercepts of that line is

  1. A \(\frac{7}{3}\)
  2. B \(1\)
  3. C \(12\)
  4. D \(\frac{26}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(12\)

Step-by-step Solution

Detailed explanation

\(m_2 = \frac{3-1}{2-1} = 2\) \(\tan 45^{\circ} = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|\) \(1 = \left| \frac{m_1 - 2}{1 + 2m_1} \right|\) \(\frac{m_1 - 2}{1 + 2m_1} = -1\) (since slope is negative) \(m_1 - 2 = -1 - 2m_1 \Rightarrow 3m_1 = 1 \Rightarrow m_1 = \frac{1}{3}\)…