Question

Find the coordinates of the points which trisect the line segment AB, if two points are A(2, 1, -3) and B (5, -8, 3).

Answer 1

Let P and Q be the points which trisect AB, Then, AP = PQ = QB

Therefore, P divides AB in the ratio 1:2 and Q divides it in the ratio 2:1

As P divides AB in the ratio 1:2, so coordinates of $P=(\frac{1\times 5+2\times 2}{1+2},\frac{1\times (-8)+2\times 1}{1+2},\frac{1\times 3+2\times (-3)}{1+2})$

$=(\frac{9}{3},\frac{-6}{3},\frac{-3}{3})=(3,-2,-1)$

Since Q divides AB in the ratio 2:1, so coordinates of $Q=(\frac{2\times 5+1\times 2}{1+2},\frac{2\times (-8)+1\times 1}{1+2},\frac{2\times 3+1\times (-3)}{1+2})=(\frac{12}{3},\frac{-15}{3},\frac{3}{3})=(4,-5,1)$

Hence, the coordinates of the points which trisect the line segment AB are P(3, -2, -1) and Q(4, -5, 1)