Question

In what ratio does the point (1, a) divide the join of (–1, 4) and (4, –1)? Also, find the value of a.

Answer 1

Let the point P (1, a) divides the line segment AB in the ratio k : 1.

Using section formula, we have:

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

`=> k + 1 = 4k - 1`

`=> 2 = 3k`

`=> k = 2/3`  ...(1)

`=>a = (-k + 4)/(k + 1)`

`=> a = (-2/3 + 4)/(2/3 + 1)`   ...(From 1)

`=> a = 10/5 = 2`

Hence, the required is 2 : 3 and the value of a is 2.