Question

Find the ratio in which the line 2x+y=4 divides the line segment joining P(2,-2) and Q(3,7)?

Answer 1

Hi there!

Let the line segment joining the points ( 2 , - 2 ) and ( 3 , 7 ) be divided  by the line 2x + y - 4 = 0 in the ratio k : 1 at P

Therefore  coordinates of the point P will be:

( 3k + 2 ) / ( k + 1 ) and ( 7k - 2 ) / ( k + 1).

But the pt. P lies on the line 2x + Y = 4 also.

Therefore,

2 ( 3k + 2 ) / ( k + 1 ) + (7k - 2 ) / ( k + 1 ) = 4

6k + 4 + 7k - 2 = 4k + 4 

9k = 2

 k = 2 / 9.

Hence,
The line segment joining the pts. ( 2, - 2 ) and ( 3, 7 ) is devided by the line 2x + y - 4 = 0 in the ratio 2 : 9

Hope it helps! :D

Cheers,
Ishaan Singh