Question

Find the co-ordinates of point which divides the line segment joining the points $A(4,-3)$ and $B(8,5)$ in the ratio 3: 1 internally.

Answer 1

If point $P$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in ratio of $m:n$, then coordinates of the point $P$ are given using Section Formula as follows:

$P=(\frac{x_{2}m+x_{1}n}{m+n},\frac{y_{2}m+y_{1}n}{m+n})$

Here $x_1=4,y_1=-3,x_2=8,y_2=5,m=3,n=1$

$P=(\frac{8\left(3\right)+4\left(1\right)}{3+1},\frac{5\left(3\right)+(-3)1}{3+1})$

$P=(\frac{24+4}{4},\frac{15-3}{4})$

$P=(\frac{28}{4},\frac{12}{4})$

$P=(7,3)$