Question

In what ratio does the x-axis divide the line segment joining the points (2, –3) and (5, 6)? Also, find the coordinates of the point of intersection.

Answer 1

Let the required ratio be $\Lambda$:1. Then, the coordinates of the point of division are,

$R(\frac{5\Lambda +2}{\Lambda +1},\frac{6\Lambda -3}{\Lambda +1}$)

But, it is a point on x-axis on which y-coordinates of every point is zero.

$\therefore \frac{6\Lambda -3}{\Lambda +1}$ = 0 $\Rightarrow \Lambda$ = $\frac{1}{2}$

Thus, the required ratio is $\frac{1}{2}:1$ or 1:2.

Substituting $\Lambda$ = $\frac{1}{2}$ in the coordinates of R. we find that its coordinates are (3, 0)