Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2, -3).

points A(4, -1) and B(-2, -3) are shown in the graph above

Now points of trisection means the points which divides the line in three parts. From the figure it is clear that, there will be 2 points which will do that. Let us call them P and Q.

Now clearly point P divides the BA in the ratio 1:2 and point Q divides the line in the ratio 2:1


⇒ Let P and Q be points of trisection

∴ P divides BA internally in ratio 1:2

Such that AP = PQ = QB

⇒ Q divides BA internally in ratio 2:1

Hence, Points of trisection are     and