Find the coordinates of the point which divides the line segment joining $(-1, 3)$ and $(4, -7)$ internally in the ratio $3 : 4$.

Given: 

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

To do: 

We have to find the coordinates of the given point.

Solution:

Let $(x, y)$ be the coordinates of the point which divides internally the line-segment joining the given points.

Here,

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

Using the division formula,

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

$( x,\ y)=( \frac{3\times4+4\times(-1)}{3+4},\ \frac{3\times(-7)+4\times3}{3+4})$

$(x,\ y)=( \frac{12-4}{7},\ \frac{-21+12}{7})$

$( x,\ y)=( \frac{8}{7},\ \frac{-9}{7})$

Therefore, $( \frac{8}{7},\ \frac{-9}{7})$ divides the line segment joining the points $(-1,\ 3)$ and $(4,\ -7)$ internally in the ratio $3 : 4$.

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Updated on: 10-Oct-2022

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