Question

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

Answer:

We have,

ABAP=31⇒AP+PBAP=31⇒3AP=AP+BP

⇒2AP=BP

⇒BPAP=21

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

∴CoordinatesofPare(1+21×5+2×2,1+21×−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