The line 2x + y - 4 = 0 divides the line segment joining A(2, -2) and B(3, 7) in the ratio
⇒ 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.