Question

The coordinates of the point which divides the line segment joining the points $(-7,4)$ and $(-6,-5)$ internally in the ratio $7:2$ is:

• A. $(\frac{56}{9},3)$
• B. $(-\frac{56}{9},-3)$
• C. $(-\frac{61}{9},2)$
• D. $(\frac{61}{9},-2)$

Answer 1

The correct option is B $(-\frac{56}{9},-3)$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(-7,4)$ and $(x_2,y_2)=(-6,-5)$ and $m=7,n=2$ in the section formula, we get
The point $(\frac{7(-6)+2(-7)}{7+2},\frac{7(-5)+2\left(4\right)}{7+2})$

$=(\frac{-56}{9},-3)$