Question

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

Answer 1

Let the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by the x-axis be k:1. 
Therefore, the coordinates of the point of division are \((\frac{-4k+1}{k+1},\frac{5k-5}{k+1})\)

We know that the y-coordinate of any point on the x-axis is 0.
Therefore, the x-axis divides it in the ratio 1:1.

Division point = \((\frac{-4(1)+1}{1+1},\frac{5(1)-5}{1+1})=\frac{-4+1}{2},\frac{5-5}{2}=(\frac{-3}{2},0)\)