Q. 243.9( 11 Votes )

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

B. 2:9

C. 2:7

D. 2 :3

Answer :

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.

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