Question

The point which divides the line segment joining the points $\left(7,-6\right)$ and $\left(3,4\right)$ in the 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

Let the coordinates of the point be $P(x,y)$ which divides the line segment joining the points $A\left(x_1,y_1\right)$ and $B\left(x_2,y_2\right)$ internally in the ratio $m_1:m_2$ are given by the formula:

$P\left(x,y\right)$ = $\left(\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}\right)$

Given , $m_1=1,m_2=2,x_1=7,x_2=3,y_1=-6,y_2=4.$

Substituting the values in the formula we get :

$$\begin{gathered} P\left(x,y\right)=\left(\frac{1\times 3+2\times 7}{1+2},\frac{1\times 4+2\times (-6)}{1+2}\right) \\ =\left(\frac{3+14}{3},\frac{4+\left(-12\right)}{3}\right) \\ =\left(\frac{17}{3},\frac{-8}{3}\right) \end{gathered}$$

Here abscissa is positive and ordinate is negative

Hence , this point will lie in fourth quadrant.