Let the area of a $ riangle 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 $O\left(2, \frac{14}{5} ight)$ and $C(c, d)$ respectively, then $c+2 d$ is equal to

Question

Let the area of a $	riangle 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 $O\left(2, \frac{14}{5}ight)$ and $C(c, d)$ respectively, then $c+2 d$ is equal to

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Equation of lines } Q R=5 x+2 y+2=0 \ & 	ext { Equation of lines } P R=10 x-3 y-38=0 \ & 	herefore 	ext { Point } R(2,-6) \ & 	ext { Centroid }=\left(\frac{5-2+2}{3}, \frac{4+4-6}{3}ight) \ & =\left(\frac{5}{3}, \frac{2}{3}ight) \ & c+2 d=\frac{5}{3}+\frac{4}{3}=3\end{aligned}$ *

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…

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