Question

31. a) Point P divides the line segment joining the points A(2, 1) and B(5,-8) such that
If P lies on the line 2x – y + k = 0, find the value of k.
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Answer 1

Answer:

Point P divides the line segment joining the points A(2, 1) and B(5, -8) such that APAB=13. If P lies on the line 2x - y + k =0,We have to find the value of k.

APAB=13⇒APAP+PB=13

⇒ 3AP = AP + PB ⇒ 2 AP = PB

⇒APPB=12⇒AP:PB=1:2

So, P divides AB in the ratio 1:2

∴ coordinates of P are

(1×5+2×21+2,1×(−8)+2×11+2)=(93,−63)=(3,−2)

Since P(3, -2) lies on 2x - y + k =0, we have

2 × 3 -(-2) + k = 0 ⇒ 6 + 2 + k =0 ⇒ = -8.

Hence, the required value of k is -8.