Question

The line segment joining A(4, 7) and B(−6, −2) is intercepted by the y – axis at the point K. write down the abscissa of the point K. hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K.

Answer 1

Since, point K lies on y-axis, its abscissa is 0.

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

We have,

`x = (k xx (-6) + 1 xx 4)/(k + 1)`

`0 = (-6k + 4)/(k + 1)`

`k = 4/6 = 2/3`

Thus, K divides AB in the ratio 2 : 3.

Also, we have:

`y = (k xx (-2) + 1 xx 7)/(k + 1)`

`y = (-2k + 7)/(k + 1)`

`y = (-2 xx 2/3 + 7)/(2/3 + 1)`

`y = (-4 + 21)/(2 + 3)`

`y = 17/5`

Thus, the co-ordinates of the point K are `(0, 17/5)`