Respuesta :
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
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Using section formula, the coordinates of first point are
[tex]Point\ 1=\left(\dfrac{1(27)+2(0)}{1+2},\dfrac{1(27)+2(0)}{1+2}\right)[/tex]
[tex]Point\ 1=\left(\dfrac{27}{3},\dfrac{27}{3}\right)[/tex]
[tex]Point\ 1=\left(9,9\right)[/tex]
Using section formula, the coordinates of first point are
[tex]Point\ 2=\left(\dfrac{2(27)+1(0)}{2+1},\dfrac{2(27)+1(0)}{2+1}\right)[/tex]
[tex]Point\ 2=\left(\dfrac{54}{3},\dfrac{54}{3}\right)[/tex]
[tex]Point\ 2=\left(18,18\right)[/tex]
Therefore, the points of trisection of the segment are (9,9) and (18,18).
