Question

Show that A (3, –2) is a point of trisection of the line segment joining the points (2, 1) and (5, −8). Also, find the co-ordinates of the other point of trisection.

Answer 1

Let A and B be the points of trisection of the line segment joining the points P (2, 1) and Q (5, −8).

So, PA = AB = BQ

We have PA : AQ = 1 : 2

Co-ordinates of the point A are

`((1 xx 5 + 2 xx 2)/(1 + 2),(1 xx (-8) + 2 xx 1)/(1 + 2))`

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

= (3, −2)

Hence, A (3, −2) is a point of trisection of PQ.

We have PB : BQ = 2 : 1

Co-ordinates of the point B are

`((2 xx 5 + 1 xx 2)/(2 + 1),(2 xx (-8) + 1 xx 1)/(2 + 1))`

`((10 + 2)/3, (-16 + 1)/3)`

= (4, −5)