Question

The line segement joining the points A(2,1) & B(5,-8) is bisected at the points P & Q where P is nearer to A. If point P lies on the line 2x -y + k = 0 find k.

Answer 1

P will divide AB in the ratio 1 : 2.
$x_1=\frac{1\left(5\right)+2\left(2\right)}{1+2}{y}_1=\frac{1(-8)+2\left(1\right)}{3}=\frac{9}{3}=3=\frac{-8+2}{3}=\frac{-6}{3}=-2$
$\Rightarrow P(3,-2)liesof2x-y+b=0\Rightarrow 2\left(3\right)-(-2)+b=0\Rightarrow 6+2+b=0\Rightarrow b=-8$