Question

Point P divides the line segment joining the points A (2, 1) and B (5, – 8) such that AP 1 = . AB 3 If P lies on the line 2x – y + k = 0, Find the value of k.

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

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