Question

The ratio in which the line segment joining the points $(3,-4)$ and $(-5,6)$ is divided by the x-axis, is

• A. $2:3$
• B. $3:2$
• C. $3:4$
• D. none of these

Answer 1

Answer: (A)

$2:3$

We know that section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

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

Give points are $(3,-4)and(-5,6)$

let x-axis divides the line segment in the ratio $r:1$

since point which is dividing the line segment lies on x-axis, y-coordinate will be $0$

y-coordinate $\frac{-4\left(1\right)+6\left(r\right)}{r+1}=0$

$6r=4$

$r=\frac{2}{3}$

Ratio$=2:3$