# The point which divides the 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

#### Complete Python Prime Pack

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack

9 Courses     2 eBooks

Given:

A point which divides the line segment joining the points $(7,\ –6)$ and $(3,\ 4)$ in ratio $1 : 2$ internally.

To do:

We have to find the quadrant in which the point lies in.

Solution:

Here $x_1=7,\ y_1=-6,\ x_2=3,\ y_2=4,\ m=1$ and $n=2$.

Using the division formula,

$( x,\ y)=( \frac{mx_2+nx_1}{m+n},\ \frac{my_2+ny_1}{m+n})$

$( x,\ y)=( \frac{1\times3+2\times7}{1+2},\ \frac{1\times4+2\times-6}{1+2})$

$( x,\ y)=( \frac{17}{3},\ \frac{-8}{3})$ which lies in IV quadrant as the x-coordinate is positive and the y-coordinate is negative.

Thus, $( \frac{17}{3},\ \frac{-8}{3})$ divides the line segment joining the points $(7,\ –6)$ and $(3,\ 4)$ in ratio $1 : 2$ internally and it lies in IV quadrant.

Updated on 10-Oct-2022 13:28:26