Question

The coordinates of the points which divides the join of $(-2,-2)$ and $(-5,7)$ in the ratio $2:1$ is:

• A. $(4,-4)$
• B. $(-3,1)$
• C. $(-4,4)$
• D. $(1,-3)$

Answer 1

The correct option is C $(-4,4)$

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 $(x_1,y_1)=(-2,-2),$ $(x_2,y_2)=(-5,7)$ and $m=2,n=1$ in the section formula, we get the point

$(\frac{2(-5)+1(-2)}{2+1},\frac{2\left(7\right)+1(-2)}{2+1})=(-4,4)$