Question

Point p lies on the line 2x+y+k=0,find the value of k if p divides the line segment joining the points A(2,-1) and b(5,-8) such that AP/AB=1/3

Answer 1

Answer:

We have,

AB

AP

=

3

1

⇒

AP+PB

AP

=

3

1

⇒3AP=AP+BP

⇒2AP=BP

⇒

BP

AP

=

2

1

So, P divides AB in the ratio 1:2.

∴CoordinatesofPare(

1+2

1×5+2×2

,

1+2

1×−8+2×1

)=(3,2)

Since,P(3,2) lies on the line 2x−y+k=0.

∴2×3−2+k=0⇒k=−4

TYPE III ON DETERMINATION OF THE TYPE OF A GIVEN QUADRILATERAL