Question

Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.

Answer 1

Let P and Q be the points of trisection of the line segment joining A(6, –9) and B(0, 0).

P divides AB in the ratio 1 : 2.

Therefore, the co-ordinates of point P are 

`((1 xx 0 + 2 xx 6)/(1 + 2),(1 xx 0 + 2 xx (-9))/(2 + 1))`

=`(12/3, (-18)/3)`

= (4, −6)

Q divides AB in the ratio 2 : 1.

Therefore, the co-ordinates of point Q are

`((2 xx 0 + 1 xx 6)/(2 + 1),(2 xx 0 + 1 xx (-9))/(2 + 1))`

= `(6/3, (-9)/3)`

= (2, –3)

Thus, the required points are (4, −6) and (2, −3).