Let the area of a P Q R with vertices P(5,4), Q(-2,4) and R(a, b) be 35 square units.

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

Accepted Answer

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

Solutions · 1