A point R with x-coordinate 4 lies on the line segment joining the points P(2, – 3, 4) and Q(8, 0, 10). Find the coordinates of the point R

A point R with x-coordinate 4 lies on the line segment joining the points P(2, - 3, 4) and Q(8, 0, 10). Find the coordinates of the point R

  1. A

    (4, -2, -6)

  2. B

    (4, 2,6)

  3. C

    (4, -2, 6)

  4. D

    None of these

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    Solution:

    Let the point R (x,y, z) divides PQ in the ratio k:1.

    k×8+1×2k+1=48k+2k+1=48k+2=4k+48k4k=424k=2k=12k:1=1:2

    Hence, the point R divides PQ internally in the ratio 1 : 2.

    Therefore, y-coordinate of R=1×0+2×(3)1+2=63=2

    and z-coordinate of R=1×10+2×41+2=10+83=183=6

    Hence, coordinate of R are (4, -2, 6).

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