Question

Pont P divides the line segment joining the points A ( 2, 1 ) and B ( 5, -8 ) such that AP / AB = 1 / 3. If P lies on the line 2x - y + k = 0, find the value of k.

Answer 1

Dear student,

Following is the answer to ypur query:

Let the coordinates of point P be P(a,b), which divides line segment AB.
Given that, AP:AB = 1:3. Therefore, AP:PB = 1:2.

Now, using section formula, $$\begin{gathered} a=\frac{5+4}{3}=3 \\ b=\frac{-8+2}{3}=-2 \end{gathered}$$
Hence, (a, b) = (3, -2)
Given that, P(a,b) lies on the line 2x - y + k = 0
Therefore, 2a - b +k = 0
6+2+k = 0
k = -8
Hence, value of k = -8.