Question

point p divided the lines segment joining the pointsA(2,1)and B (5,-8)such that AP/AB =1/3,if p lies on the line 2x+y+k=0 find the value of K

Answer 1

A(2,1)=(x1,y1)
B(5,-8)=(x2,y2)

AP/AB= 1/3
AP/PB= 1/2
THEREFORE, M=1 N=2
P(x,y)= Mx1+Nx2/M+N, My1+Ny2/M+N
therefore ,
P(x,y)= (4,-5)
as 2x+y+k=0
k=-(2x+y)
k=-3