Question

the line joining the points 2 ,-1 and 5, -6 is bisected at p .P lies on 2x+4y+k=0 find k​

Answer 1

Let P=(x, y)

Using Midpoint formula,

$x = \frac{x1 + x2}{2} ,y = \frac{y1 + y2}{2} \\ x = \frac{2 + 5}{2} ,y = \frac{ - 1 - 6}{2} \\ x = \frac{7}{2} ,y = - \frac{7}{2}$

Since point P is lying on 2x+4y+k = 0

∴ At $( \frac{7}{2} , - \frac{7}{2} )$

$2( \frac{7}{2} ) + 4( - \frac{7}{2} ) + k = 0 \\ 7 - 14 + k = 0 \\ - 7 + k = 0 \\ ∴k = 7$