Question

The line segment joining the points M(5, 7) and N(–3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

Answer 1

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

Let the co-ordinates of point L be (0, y).

Let L divides MN in the ratio k : 1.

Using section formula, we have:

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

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

`-3k + 5 = 0`

`k = 5/3`

Thus, the required ratio is 5 : 3.

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

= `(5/3 xx 2 + 7)/(5/3 + 1)`

= `(10 + 21)/(5 + 3)`

= `31/8`

L = `(0, 31/8)`