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

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Using section formula, the coordinates of first point are

$Point\ 1=\left(\dfrac{1(27)+2(0)}{1+2},\dfrac{1(27)+2(0)}{1+2}\right)$

$Point\ 1=\left(\dfrac{27}{3},\dfrac{27}{3}\right)$

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

Using section formula, the coordinates of first point are

$Point\ 2=\left(\dfrac{2(27)+1(0)}{2+1},\dfrac{2(27)+1(0)}{2+1}\right)$

$Point\ 2=\left(\dfrac{54}{3},\dfrac{54}{3}\right)$

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

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