Question

Find the ratio in which the line joining (-2, 5) and (-5,-6) is divided by the line 2x+y=-4.Hence find the point of intersection.

Answer 1

Solution

Given :-

• point of line joining , p(-2,5) & q(-5,-6)
• Equation of line , 2x + y = -4 _______(1)

Find :-

• Intersection point of both line

Explanation

Let, the line 2x + y = -4 ___(1), devide the line statement joining the point P(-2,5) & q(-5 , -6) in the ratio m : 1.

Let, the intersection point be O.

then,

Co-ordinatotr of O given by,

= O[ {m(y") + 1(y')}/(m + 1) , {m(x") + 1(x')}/(m + 1) ]

Where,

• x ' = -2
• x" = -5
• y' = 5
• y" = -6

So, Now

==> O[ m(-6) + (5)}/(m + 1) , { m(-5) + (-2)}/(m + 1)]

==> O[ (-6m + 5)/(m + 1) , ( -5m - 2)/(m + 1) ]

Here, O interesect line 2x + y = -4

Then,

==.> 2[ -6m + 5)/(m + 1) ] + (-5m - 2)/(m + 1) = -4

==> -12m + 10 - 5m - 2 = -4(m + 1)

==> -17m + 8 = -4m - 4

==> -17m + 4m = -4 - 8

==> -13m = -12

==> m = 12/13

Or,

==> m:1 = 12:13

Hence

• Ratio will be = 12:13

_______________