Question

In what ratio does the point (a, 6) divide the join of (–4, 3) and (2, 8)? Also, find the value of a.

Answer 1

Let the point P (a, 6) divides the line segment joining A (–4, 3) and B (2, 8) in the ratio k : 1.

Using section formula, we have:

`6 = (8k + 3)/(k + 1)`

`=> 6k + 6 = 8k + 3`

`=>3 = 2k`

`=> k = 3/2`  ...(1)

`=>a = (2k - 4)/(k + 1)`

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

`=> a = -2/5`

Hence, the required ratio is 3 : 2 and the value of a is `-2/5`