Let the area of a P Q R with vertices P(5,4), Q(-2,4) and R(a, b)… - Vidyadip

MCQ

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
$\frac{7}{3}$
✓
3
C
2
D
$\frac{8}{3}$

✓

Answer

Correct option: B.

3

(B)

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

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