Question

Determine the ratio in which the line 2x + y = 6 divides the line segment joining the points (1, 3) and (2, 5).

Answer 1

Given:

Points A(1, 3) and B(2, 5)

Line equation: 2x + y – 6 = 0

Let the line divide AB in the ratio k : 1 at point P(x, y).

Using section formula:

`x = (k(2) + 1(1))/(k + 1)`

= `(2k + 1)/(k + 1)`

`y = (k(5) + 1(3))/(k + 1)`

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

Since P lies on 2x + y – 6 = 0:

`2((2k + 1)/(k + 1)) + ((5k + 3)/(k + 1)) - 6 = 0`

4k + 2 + 5k + 3 – 6(k + 1) = 0

9k + 5 – 6k – 6 = 0

3k – 1 = 0

`k = 1/3`

Ratio is 1 : 3