Question

The line joining the points (2,-1) and (5,-6) is bisected at P. If P lies on the line 2x+4y+K=0, find the value of K

Answer 1

k = 7

Explanation:

Find the coordinates of P using the midpoint formula

P = [
`(1)/(2)`(2 + 5),
`(1)/(2)`(- 1 - 6) ]

= (
`(7)/(2)`, -
`(7)/(2)`)

Since the line passes through P the the coordinates of P make the equation true.

Substitute the coordinates of P into the equation

2 ×
`(7)/(2)` + 4 × -
`(7)/(2)` + k = 0, that is

7 - 14 + k = 0

- 7 + k = 0 ( add 7 to both sides )

k = 7