Question

Find the ratio in which line segment joining points A (1, - 5) and B (- 4, 5) is divided by x-axis. Also, find coordinates of the point of division.

Answer 1

Let the ratio in which line segment joining the points A (1, - 5) and B (- 4, 5) is divided by x-axis be K:1 .
Therefore, coordinates of the point of division C is $(\frac{-4k+1}{k+1},\frac{5k-5}{k+1})$
We know that y-coordinate of any point on x-axis is 0
$\therefore \frac{5k-5}{k+1}=0$
5k - 5 = 0
k = 1
Therefore, x-axis divides it in the ratio 1 : 1

$C=(\frac{-4\left(1\right)+1}{1+1},\frac{5\left(1\right)-5}{1+1})=(\frac{-4+1}{2},\frac{5-5}{2})=(\frac{-3}{2},0)$