Question

Find the coordinates of the points which trisect the line joining the points P(4,0,1) and Q(2,4,0)

Answer 1

Answer:

The points of trisectiion are

$(\frac{10}{3},\frac{4}{3},\frac{2}{3})\:and\:(\frac{8}{3},\frac{8}{3},\frac{1}{3})$

Step-by-step explanation:

Find the coordinates of the points which trisect the line joining the points P(4,0,1) and Q(2,4,0)

Formula used:

The co ordinates of the point which divides the line segment joining $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ internally in the ratio m:n is}[/tex]

$\boxed{(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n})}$

Given: P(4,0,1) and Q(2,4,0)

Let L and M be the points of trisection of line joining P and Q.

Clearly, the point L divides PQ internally in the ratio 1:2

Then, L is

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n})$

$L\:is\:(\frac{1(2)+2(4)}{1+2},\frac{1(4)+2(0)}{1+2},\frac{1(0)+2(1)}{1+2})$

$\implies\:L\:is\:(\frac{10}{3},\frac{4}{3},\frac{2}{3})$

similarly, the point M divides PQ internally in the ratio 2:1

Then M is

$M\:is\:(\frac{2(2)+1(4)}{2+1},\frac{2(4)+1(0)}{2+1},\frac{2(0)+1(1)}{2+1})$

$\implies\:M\:is\:(\frac{8}{3},\frac{8}{3},\frac{1}{3})$

$\therefore\text{The points of trisection are}$

$\boxed{(\frac{10}{3},\frac{4}{3},\frac{2}{3})\:and\:(\frac{8}{3},\frac{8}{3},\frac{1}{3})}$