Question

In what ratio is a line segment joining the points (-2, -3) and (3, 7) divided by y-axis?

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{4}{5}$
• D. $\frac{5}{4}$

Answer 1

The correct option is A $\frac{2}{3}$

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 $(x_1,y_1)=(-2,-3)$ and $(x_2,y_2)=(3,7)$ in the section formula, we get the point $(\frac{m\left(3\right)+n(-2)}{m+n},\frac{m\left(7\right)+n(-3)}{m+n})=(\frac{3m-2n}{m+n},\frac{7m-3n}{m+n})$

As the
point lies on y - axis, x -coordinate $=0$.

$=>\frac{3m-2n}{m+n}=0$
$=>3m=2n$ or $m:n=2:3$