The joint P (5, - 3) is one of the two points of trisection of line segment joining the points A (7, - 2) and B (1, - 5).

Question

State whether the following statement are true or false. Justify your answer.

The joint P (5, - 3) is one of the two points of trisection of line segment joining the points A (7, - 2) and B (1, - 5).

Answer 1

True

Let P (5, - 3) be the point which divides the line segment joining the points A (7, - 2) and B (1, - 5) in the ratio k:1 internally.

By using the section formula,

The coordinate of point P

⇒ k + 7 = 5k + 5

⇒ - 4k = - 2

∴ k = 1/2

So the point P divides the line segment AB in ratio 1:2

Hence, Point P in the point of trisection of AB.