Question

In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.

Answer 1

Let AB be divided by the x-axis in the ratio k :1 at the point P. 

Then, by section formula the coordination of P are

Therefore, the required ratio is 1/2 :1, which is same as 1 : 2

Thus, the x-axis divides the line AB in the ratio 1 : 2 at the point P.

Applying k = 1/2 we get the coordinates of point.

Hence, the point of intersection of AB and the x-axis is P (3, 0).