Question

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

Answer 1

Answer:

Given AP/AB = 2/3

AB/AP = 3/2

Substracting 1 both sides. we get

(AB - AP)/AP = (3 - 2)/2

BP/AP = 1/2

So P divide AB in 2:1

Coordinate of P =

$( \frac{2 \times 5 + 1 \times 2}{2 + 1} \: \: . \: \: \frac{2 \times ( - 8) + 1 \times 1}{2 + 1} ) = (4 \: \: . \: \: - 5)$

so P(4 , -5) lies on 2x - y + k = 0

i.e

$2 \times 4 - ( - 5) + k = 0$

K = - 13 Ans.

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