Question

Find the co-ordinates of the points of tri-section of the line joining the points (–3, 0) and (6, 6).

Answer 1

Let P and Q be the point of trisection of the line segment joining the points A (–3, 0) and B (6, 6).

So, AP = PQ = QB

We have AP : PB = 1 : 2

Co-ordinates of the point P are

`((1 xx 6 + 2 xx (-3))/(1 + 2),(1 xx 6 + 2 xx 0)/(1 + 2))`

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

= (0, 2)

We have AQ : QB = 2 : 1

Co-ordinates of the point Q are

`((2 xx 6 + 1 xx (-3))/(2 + 1),(2 xx 6 + 1 xx 0)/(2 + 1))`

= `((9)/3, 12/3)`

= (3, 4)