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AP EAMCET · Maths · Straight Lines

If \((\alpha, \beta)\) is the orthocentre of the triangle with the vertices \((2,2),(5,1),(4,4)\), then \(\alpha+\beta=\)

  1. A 6
  2. B 5
  3. C \(\frac{5}{2}\)
  4. D \(\frac{7}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) 6

Step-by-step Solution

Detailed explanation

\(\mathrm{A}(2,2), \mathrm{B}(5,1), \mathrm{C}(4,4)\) Slope of \(A B=\frac{1-2}{5-2}=\frac{-1}{3}\) \(\therefore\) Equation of CG \(\begin{aligned} & y-4=3(x-4) \\ & \Rightarrow 3 x-y=8 \end{aligned}\) Slope of \(A C=\frac{4-2}{4-2}=1\) \(\therefore\) Equation of BF…