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AP EAMCET20227 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

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=

Options

  1. A26
  2. B25
  3. C24
  4. D34

Correct answer

D. 34

Step-by-step solution

Centroid of triangle with vertices (4, p,-3),(-1,-1,2),(3,5,-8) is ( 4-1+3 3 , p-1+5 3 , -3+2-8 3 ) which is (2, 4+p 3 ,-3 ) . Mid-point of (1,4,-2)(q, 2,-4) is ( 1+q 2 , 3,-3 ) As both points are, array rlrl & & 2 & = 1+q 2 and 4+p 3 =3 & p & =5, q=3 & p^2+q^2 & =25+9=34 array

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