TS EAMCET · Maths · Straight Lines
\((-2,-1),(2,5)\) are two vertices of a triangle and \(\left(2, \frac{5}{3}\right)\) is its orthocenter. If \((m, n)\) is the third vertex of that triangle then \(m+n=\)
- A -4
- B -2
- C 5
- D 8
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
\(A=(-2,-1)\), \(B=(2,5)\), \(C=(m,n)\), \(H=\left(2, \frac{5}{3}\right)\) Since \(x_B = x_H = 2\), line BH is vertical. Therefore, the side AC must be horizontal, implying \(y_A = y_C\). \(n = -1\) Slope of AB, \(m_{AB} = \frac{5 - (-1)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2}\)…
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