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