Question

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

Answer 1

We are given,

$(x_1,y_1)=(4,-3)$ & $1(x_2,y_2)=(8,5)$

Let (x,y)coordinates which divides the line joining the point $(x_1,y_1)$

and $(x_2,y_2)$ in ratio $m:n=3:1$ internally.

So,$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

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

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

$(x,y)=(7,3)$