Question

The line segment joining A (2, 3) and B (6, –5) is intercepted by x-axis at the point K. Write down the ordinate of the point K. Hence, find the ratio in which K divides AB. Also, find the coordinates of the point K.

Answer 1

Since, point K lies on x-axis, its ordinate is 0.

Let the point K (x, 0) divides AB in the ratio k : 1.

We have,

`y = (k xx (-5) + 1 xx 3)/(k + 1)`

`0 = (-5k + 3)/(k + 1)`

`k = 3/5`

Thus, K divides AB in the ratio 3 : 5.

Also, we have:

`x = (k xx 6 + 1 xx 2)/(k + 1)`

`x = (3/5 xx 6 + 2)/(3/5 + 1)`

`x = (18 + 10)/(3 + 5)`

`x = 28/8 = 7/2 = 3 1/2`

Thus, the co-ordinates of the point K are `(3 1/2, 0)`.