Question

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

Answer 1

Let R and S be two point which trisect the join of PQ.

$\therefore$ $PR=RS=SQ$

$\therefore$ Point R divides the join of PQ in the ratio 1 : 2

$\therefore$ Coordinates of R is

$(\frac{1\times 10+2\times 4}{1+2},\frac{1\times -16+2\times 2}{1+2},\frac{2\times 6+2\times -6}{1+2})$

= $(6,-4,-2)$

Also point S divides the join of PQ in the ratio 2 : 1

$\therefore$ Coordinates of S is

$(\frac{2\times 10+1\times 4}{1+2},\frac{2\times -16+1\times 2}{1+2},\frac{2\times 6+1\times -6}{1+2})$

= $(8,-10,2).$