The line segment joining any two points (x₁, y₁) and (x₂, y₂) y₂ is given as:

⇒

⇒ y + 1 = 10/5 (x-3)

⇒ y + 1 = 2(x-3)

⇒ y + 1 = 2x – 6
⇒ 2x – y = 7..eq(1) is the equation of line segment.

Now, we have to find the point of intersection of eq (1) & the given line: x – y- 2 = 0

2x – y = 7

& x – y – 2 = 0

2x – 7 = x – 2

⇒ x = 7- 2

⇒ x = 5

And, y = 3

Let us say this point divides the line segment in the ratio of k₁:k₂

Then,

⇒ 5k₁ + 5k₂ = 8k₁ + 3k₂

⇒ 5k₁ - 8k₁ + 5k₂ - 3k₂= 0

⇒ -3k₁ + 2k₂ = 0

⇒