AP EAMCET · Maths · Three Dimensional Geometry
If the centroid of a triangle with vertices \((4, p,-3),(-1,-1,2)\) and \((3,5,-8)\) is given by mid-point of \((1,4,-2)\) and \((q, 2,-4)\), then \(p^2+q^2=\)
- A \(26\)
- B \(25\)
- C \(24\)
- D \(34\)
Answer & Solution
Correct Answer
(D) \(34\)
Step-by-step Solution
Detailed explanation
Centroid of triangle with vertices \((4, p,-3),(-1,-1,2),(3,5,-8)\) is \[ \left(\frac{4-1+3}{3}, \frac{p-1+5}{3}, \frac{-3+2-8}{3}\right) \] which is \(\left(2, \frac{4+p}{3},-3\right)\). Mid-point of \((1,4,-2)(q, 2,-4)\) is \(\left(\frac{1+q}{2}, 3,-3\right)\) As both points…
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