Question

The point which divides line segment joining the 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

The correct option is D IV quadrant

Using the section formula, if a point $(x,y)$ divides the line joining the
points $(x_1,y_1)$ and $(x_2,y_2)$ internally in the
ratio $m:n$, then $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(7,-6)$ and $(x_2,y_2)=(3,4)$ and $m=1,n=2$ in the section formula, we get
the point $(\frac{1\left(3\right)+2\left(7\right)}{1+2},\frac{1\left(4\right)+2(-6)}{1+2})=(\frac{17}{3},\frac{-8}{3})$

Since, $x-$ cordinate is positive and $y-$ cordinate is negative, the point lies in the $IV$ quadrant.