MHT CET · Maths · Straight Lines
If \(A \equiv(5,1, p), B \equiv(1, q, p)\) and \(C \equiv(1,-2,3)\) are vertices of the triangle and \(G \equiv\left(r,-\frac{4}{3}, \frac{1}{3}\right)\) is its centroid, then the values of \(p, q, r\) are respectively
- A \(-1,3, \frac{7}{3}\)
- B \(1,3, \frac{7}{3}\)
- C \(1,-3, \frac{7}{3}\)
- D \(-1,-3, \frac{7}{3}\)
Answer & Solution
Correct Answer
(D) \(-1,-3, \frac{7}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \left(r, \frac{-4}{3}, \frac{1}{3}\right) \equiv\left(\frac{5+1+1}{3}, \frac{1+q-2}{3}, \frac{p+p+3}{3}\right) \\ & \Rightarrow r=\frac{7}{3}, \frac{-4}{3}=\frac{q-1}{3}, \frac{1}{3}=\frac{2 p+3}{3} \\ & \Rightarrow p=-1, q=-3, r=\frac{7}{3}\end{aligned}\)
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