# Find the coordinates of the point which divides the join of $(-1, 7)$ and $(4, -3)$ in the ratio $2: 3$.

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Given:

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

To do:

We have to find the coordinates of the given point.

Solution:

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

Here,

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

Using the division formula,

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

$P( x,\ y)=( \frac{2\times4+3\times(-1)}{2+3},\ \frac{2\times(-3)+3\times7}{2+3})$

$(x,\ y)=( \frac{8-3}{5},\ \frac{-6+21}{5})$

$( x,\ y)=( \frac{5}{5},\ \frac{15}{5})$

$(x,\ y)=(1, 3)$

Therefore, $( 1,\ 3)$ divides the line segment joining the points $(-1,\ 7)$ and $(4,\ -3)$ internally in the ratio $2 : 3$.

Updated on 10-Oct-2022 13:22:05