Question

In what ratio does the point $(-3,y)$ divide the join of $(-5,11)$ and $(4,-7)$ .

• A. $\frac{2}{7}:1$
• B. $\frac{6}{7}:1$
• C. $\frac{3}{7}:1$
• D. None of these

Answer 1

The correct option is A $\frac{2}{7}:1$

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

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

Let point divide in $m:1$ ratio

$\Rightarrow \frac{(-5\times 1)+(4\times m)}{m+1}=-3\Rightarrow -5+4m=-3m-3$

$\Rightarrow m=\frac{2}{7}$

$\therefore \frac{2}{7}:1$