Find the coordinates of the points which tisect the line segment … - Vidyadip

Question

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

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Answer

Tri section points are those which divide line in ratio 1 : 2 or 2 : 1
P(4, 2, -6) and Q(10, -16, 6)
Consider 1 : 2 case, we get
$\Big(\frac{10+8}{3},\frac{-16+4}{3},\frac{6–12}{3}\Big)= (6, -4, -2)$
Consider 2 : 1 case, we get
$\Big(\frac{20+4}{3},\frac{-32+2}{3},\frac{12-6}{3}\Big)=(8, -10, 2)$
(6, -4, -2) and (8, -10, 2) are tri section points.

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