JEE Mains · Maths · STD 11 - 9. straight line
Let the area of a \(\triangle P Q R\) with vertices \(P(5,4), Q(-2,4)\) and \(R(a, b)\) be 35 square units. If its orthocenter and centroid are \(O\left(2, \frac{14}{5}\right)\) and \(C(c, d)\) respectively, then \(c+2 d\) is equal to
- A \(\frac{8}{3}\)
- B \(\frac{7}{3}\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Equation of lines } Q R=5 x+2 y+2=0 \\ & \text { Equation of lines } P R=10 x-3 y-38=0 \\ & \therefore \text { Point } R(2,-6) \\ & \text { Centroid }=\left(\frac{5-2+2}{3}, \frac{4+4-6}{3}\right) \\ & =\left(\frac{5}{3}, \frac{2}{3}\right) \\ & c+2…
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