# Point P divides the line segment joining the points A ( 2,1 ) and B ( 5, -8 ) such that AP : AB = 1: 3. IF P lies 2x - y + k = 0 , then the value of k.

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by 426ri543

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by 426ri543

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now,co ordinate of P = (mx2 + nx1 / m+n , my2 + ny1 / m+n ).

=(5+6/4 , -8+3/4)

=(11/4 , -5/4).

therefore, P in X axis is 11/4 and and in Y axis is -5/3.

as they satisfy2X -Y + K=0

=2×11/4 -(-5/4)+ K = 0

=11/2 + 5/3 + K = 0

= 33+10+6k=0 (by taking lcm)

= 6k = -43

therfore k = -43/6.

The Brainliest Answer!

Given AP:AB-1:3

SO,AP:PB=1:2

GIVEN THAT P is lie on 2x-y+k=0

2(3)-(-2)+k=0

⇒6+2+k=0

⇒8+k =0

⇒k=-8

SO,AP:PB=1:2

GIVEN THAT P is lie on 2x-y+k=0

2(3)-(-2)+k=0

⇒6+2+k=0

⇒8+k =0

⇒k=-8