The line 2x + y - A. 2 :5

B. 2:9

C. 2:7

D. 2 :3

⇒ Let 2x + y = 4 ………….. (1)

Finding the equation of line formed by AB:

Finding slope:

⇒

⇒

⇒ m = 9

The equation of line AB:

⇒ y – y₁ = m×(x-x₁)

⇒ y-(-2) = 9×(x-2)

⇒ y + 2 = 9x – 18

⇒ 9x – y = 20……………… (2)

When we solve the two equations simultaneously, we get point of intersection of two lines.

⇒ Adding (1) and (2)

⇒ 11x = 24

⇒ x = 24/11

⇒ Substituting the value of x in (1)

⇒ 2×24/11 + y = 4

⇒ y = 4 – 48/11

⇒ y = -4/11

let us assume the line divides the segment AB in the ratio k:1

Then by section formula, the coordinates of point which divide the line AB is given as

Since we know x-coordinate of the point

⇒

⇒ 33k + 22 = 24k + 24

⇒ 9k = 2

⇒ k = 2:9

Therefore the line 2x + y -4 = 0 divides the line segment AB into the ratio 2:9.