Question

What are the points of trisection of the segment with endpoints (0,0) and (27,27) ?

Answer 1

Given:

Endpoints of a segment are (0,0) and (27,27).

To find:

The points of trisection of the segment.

Solution:

Points of trisection means 2 points between the segment which divide the segment in 3 equal parts.

First point divide the segment in 1:2 and second point divide the segment in 2:1.

Section formula: If a point divides a line segment in m:n, then

`Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

Using section formula, the coordinates of first point are

`Point\ 1=\left((1(27)+2(0))/(1+2),(1(27)+2(0))/(1+2)\right)`

`Point\ 1=\left((27)/(3),(27)/(3)\right)`

`Point\ 1=\left(9,9\right)`

Using section formula, the coordinates of first point are

`Point\ 2=\left((2(27)+1(0))/(2+1),(2(27)+1(0))/(2+1)\right)`

`Point\ 2=\left((54)/(3),(54)/(3)\right)`

`Point\ 2=\left(18,18\right)`

Therefore, the points of trisection of the segment are (9,9) and (18,18).