AP EAMCET · Maths · Straight Lines
\(A(3,2,-1), B(4,1,1), C(6,2,5)\) are three points. If \(D, E, F\) are three points which divide \(B C\), \(C A, A B\) respectively in the same ratio \(2: 1\), then the centroid of \(\triangle D E F\) is
- A \(\left(\frac{13}{3}, \frac{5}{3}, \frac{5}{3}\right)\)
- B \((13,5,5)\)
- C \((4,2,1)\)
- D \(\left(\frac{11}{3}, \frac{4}{3}, \frac{1}{3}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{13}{3}, \frac{5}{3}, \frac{5}{3}\right)\)
Step-by-step Solution
Detailed explanation
Here, \(D=\left(\frac{2 \times 6+4 \times 1}{3}, \frac{2 \times 2+1 \times 1}{3}, \frac{2 \times 5+1 \times 1}{3}\right)\) \(=\left(\frac{16}{3}, \frac{5}{3}, \frac{11}{3}\right)\) Similarly,…
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