Find the coordinates of the points which trisect the line segment joining the points P(4,2, – 6) and Q(10, – 16,6).

Find the coordinates of the points which trisect the line segment joining the points P(4,2, - 6) and Q(10, - 16,6).

  1. A

    (6, - 4, - 2), (8, - 10, 2)

  2. B

    (6, 4, - 2), (8, - 10, 2)

  3. C

    (6, - 4, - 2), (8, 10, 2)

  4. D

    None of the above

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    Solution:

    Let the point R1, trisects the line PQ i.e., it divides the line in the ratio 1:2

    R1=1×10+2×41+2,1×(16)+2×21+2,1×6+2×(6)1+2=10+83,16+43,6123=183,123,63=(6,4,2)

    Again, let the point R2 divides PQ internally in the ratio 2: 1. Then, 

     R2=2×10+1×42+1,2×(16)+1×22+1,2×6+1×(6)1+2=20+43,32+23,1263=243,303,63=(8,10,2)

    Hence, required points are (6,-4, - 2) and (8, - 10,2). 

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