Question

Question 9
The point which divides the line segment joining points (7, - 6) and (3,4) in ratio 1:2 internally lies in the
(A) I quadrant
(B) II quadrant
(C) III quadrant
(D) IV quadrant

Answer 1

If P(x,y) divides the line segment joining points A$(x_1,y_1)$ and B$(x_2,y_2)$ internally in the ratio $m:n,$
then, $x=\frac{m{x}_2+n{x}_1}{m+n}andy=\frac{m{y}_2+n{x}_1}{m+n}$

$Given:x_1=7,y_1=-6,x_2=3,y_2=4,m=1andn=2$

$\therefore x=\frac{1\left(3\right)+2\left(7\right)}{1+2},y=\frac{1\left(4\right)+2(-6)}{1+2}\text{[by section formula]}\Rightarrow x=\frac{3+14}{3},y=\frac{4-12}{3}\Rightarrow x=\frac{17}{3},y=-\frac{8}{3}$