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

Answer:

k = 7

Step-by-step explanation:

Find the coordinates of P using the midpoint formula

P = [$\frac{1}{2}$(2 + 5), $\frac{1}{2}$(- 1 - 6) ]

  = ( $\frac{7}{2}$,  - $\frac{7}{2}$)

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

Substitute the coordinates of P into the equation

2 × $\frac{7}{2}$ + 4 × - $\frac{7}{2}$ + k = 0, that is

7 - 14 + k = 0

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

k = 7