Question

The point which divides internally , the line joining $(-3,-4)$ to $(-8,7)$ in the ratio $7:5$ is

Answer 1

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

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

Since, $m:n=7:5$

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

$P(x,y)=\frac{(7\times -8)+(5\times -3)}{7+5},\frac{(7\times 7)+(5\times -4)}{7+5}$

$=\frac{-56-15}{12},\frac{49-20}{12}$

$=\frac{-71}{12},\frac{29}{12}$