Question

Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.

Answer 1

Let AB be the line segment between the axes such that point R (h, k) divides AB in the ratio 1: 2.

Let the respective coordinates of A and B be (x, 0) and (0, y).
Since point R (h, k) divides AB in the ratio 1: 2, according to the section formula,

Therefore, the respective coordinates of A and B are [ 3h/2,0 ] and (0, 3k).

Now, the equation of line AB passing through points [3h/2,0 ] and (0, 3k) is

Thus, the required equation of the line is 2kx + hy = 3hk