Question

The line segment joining the points (-3, -4) and (1, -2) is divided by the y-axis in the ratio

• A. 1 : 3
• B. 3 : 1
• C. 2 : 3
• D. 3 : 2

Answer 1

The correct option is B 3 : 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 $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Substituting $(x_1,y_1)=(-3,-4)$ and $(x_2,y_2)=(1,-2)$ in the section formula, we get the point $(\frac{m\left(1\right)+n(-3)}{m+n},\frac{m(-2)+n(-4)}{m+n})=(\frac{m-3n}{m+n},\frac{-2m-4n}{m+n})$

As the point lies on y - axis, x -coordinate $=0$.
$=>\frac{m-3n}{m+n}=0$
$=>m=3n$ or $m:n=3:1$