Determine the ratio in which the line 2x+y-4=0 divides the line segment joining point A(2,-2) & B(3,7)?

its like this

a²b²x² + b²x - a²x -1 = 0

=> b²x  ( a²x  + 1 ) - 1 ( a²x + 1 ) = 0

=> ( a²x + 1 ) ( b²x - 1 ) = 0

=> x = -1/a² ,or 1/b^2. 

Ans. 3 

centroid will be { ( 2 + 1 + c2) / 3 ,  ( a + b - 3 ) /3 } , these corodinates  are not zero. So none of them will be on x-axis or y-axis. 

To get the ordinate on y-axis, a + b = 3

Ans. 1

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 pt. 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. 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

Let P (m,n) be the point of intersection of both the lines.

Now using (y - y1) = [(y2 - y1)/(x2 - x1)] x (x - x1), find the equation of the line AB

now, solve botht the equtions to find the value of x,y

Now, this Q(x,y) is the point of intersection of both the points and then calculate the ratio

in which it divides the line ..... AB

using, x = m(x2) + n(x1) / (m + n) and y = m(y2) + n(y1)/ (m + n)

this kills the problem

Let the ratio be K:1 .

X = ( 3k + 2 ) / k + 1

Y = ( 7k - 2 ) / k + 1

2x + y - 4 = 0

On putting value of x and y --->

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

=>  6k + 4 + 7k - 2  = 4k + 4

=>  9k = 2

=>  k = 2 / 9 

Hence ratio = 2:9

Pls verify !!

Pls verify !!

take d ratio as k:1...u will gt (x,y) as( -1,1/2)..so then substitute it in the equation !!!!!

no actuly its wrong !!