Question

Find the ratio in which the line segment joining the points A (3, -3) and B (-2, 7) is divided by x-axis. Also, find the coordinates of the point of division.

Answer 1

Let the point (x,0) on x-axis divide the line segment joining the points A (3, -3) and B (-2, 7) in the ratio a:1.

$y=\frac{a{y}_2+y_1}{a+1}$

$\Rightarrow 0=\frac{7a-3}{a+1}$

$\Rightarrow a=\frac{3}{7}$

Now, for the x-coordinate

$x=\frac{a{x}_2+x_1}{a+1}$

$\Rightarrow x=\frac{-2\times \frac{3}{7}+3}{\frac{3}{7}+1}=\frac{3}{2}$

So, the coordinate of the point of division is $\frac{3}{2},0$.