Question

Find the co-ordinates of the points of trisection of the line segment joining the points (−2, 2) and (7, −4).

Answer 1

Given the points are (−2, 2) and (7, −4)

Let the points of trisection be A and B

Using the section formula, we have,

Coordinates of A are as:

${\displaystyle \left[\left(\frac{1\left(7\right)+2(-2)}{1+2}\right)\text{,}\left(\frac{1(-4)+2\left(2\right)}{1+2}\right)\right]}$

= ${\displaystyle \left[\left(\frac{3}{3}\right)\text{,}\left(\frac{0}{3}\right)\right]}$

= (1, 0)

Now, the coordinates of B are as:

${\displaystyle [\frac{2\left(7\right)+1(-2)}{2+1},\left(\frac{2(-4)+1\left(2\right)}{2+1}\right)]}$

= ${\displaystyle \left[\left(\frac{12}{3}\right)\text{,}\left(\frac{-6}{3}\right)\right]}$

= (4, −2)

Hence, the co-ordinates of points of trisection are (1, 0) and (4, −2).