Question

Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7)

Answer 1

Suppose the line 3x + y – 9 = 0 divides the line segment joining A (1, 3) and B(2, 7) in the ratio k : 1 at point C. Then, the coordinates of C are

`( \frac{2k+1}{k+1},\ \frac{7k+3}{k+1})`

But, C lies on 3x + y – 9 = 0. Therefore,

`3( \frac{2k+1}{k+1})+\frac{7k+3}{k+1}-9=0`

⇒ 6k + 3 + 7k + 3 – 9k – 9 = 0

`⇒ k = \frac { 3 }{ 4 }`

So, the required ratio is 3 : 4 internally

Type III : On determination of the type of a given quadrilateral