Question

The line joining the points (2, 1) and (5, –8) is trisected by the points P and Q. If the point P lies on the line 2x – y + k = 0, find the value of k.

Answer 1

As line segment AB is trisected by the points P and Q. Therefore,
Case I: When AP : PB = 1 : 2.
Then, coordinates of P are

⇒ P (3, –2)

Since the point P (3, – 2) lies on the line

Case II: When AP : PB = 2 : 1.
Coordinates of point P are