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Introduction to Three Dimensional Geometry · Class 11 · CBSE · Science Mathematics

The point P divides the line segment joining A(-1, 2, 4) and B(5, -4, -2) internally in the ratio AP:PB = 2:1. The coordinates of P are:

Practice question from Introduction to Three Dimensional Geometry (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-10E1FE

The point P divides the line segment joining A(-1, 2, 4) and B(5, -4, -2) internally in the ratio AP:PB = 2:1. The coordinates of P are:

  1. A.(1, -2, 0)
  2. B.(3, -2, 0)Correct answer
  3. C.(3, 0, 2)
  4. D.(2, -1, 1)

Solution

For internal division in the ratio m:nm:n, the point is (nx1+mx2m+n,ny1+my2m+n,nz1+mz2m+n)\left(\frac{nx_1+mx_2}{m+n},\frac{ny_1+my_2}{m+n},\frac{nz_1+mz_2}{m+n}\right). Here m=2m=2 and n=1n=1, so P=(−1+103,2−83,4−43)=(3,−2,0)P=\left(\frac{-1+10}{3},\frac{2-8}{3},\frac{4-4}{3}\right)=(3,-2,0).

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