Question

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

Answer 1

Key concept: Section formula

`(x,y) = (mx_2 +nx_1)/(m+n), (my_2 + ny_1)/(m+n)`

`p(x,y) = (1(5)+2(2))/(1+2), (1(-8)+2(1))/(1+2)`

`x = (5+4)/3`

`x=9/3`

x = 3

`y = (-8+2)/3`

`y = (-6)/3`

y = −2

2x − y + k = 0     (x = 3, y = −2)

2(3) − (−2) + k = 0

6 + 2 + k = 0

k = −8