Question

Find the ratio in which the point `(8/5, y)` divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.

Answer 1

Let P divide the line segment AB in the ratio k : 1

Then, by section formula,

`8/5 = (2k + 1)/(k + 1)`   ...(i)

And `y = (3k + 2)/(k + 1)`   ...(ii)

From (i), we get

8k + 8 = 10k + 5

2k = 3

⇒ `k = 3/2`

From (ii), we get

`y = (3(3/2) + 2)/(3/2 + 1)`

= `(9 + 4)/5`

= `13/5`

Therefore, the required ratio is 3 : 2 value of `y = 13/5`.