Question

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 on the line 2x - y + k = 0, find the value of k.​

Answer 1

AP:AB=1:3

AP=a

AB=3a

therefore

AP:PB=1:2

AP=a=m

PB=2a=n

A=(x1,y1)=(2,1)

B=(x2,y2)=(5,-8)

therefore by using the formula (sorry but i forgot the name of the formula ... :))

(plz refer NCERT . It is beside midpoint formula)

P=(x,y)=(mx2+nx1/m+n,my2+ny1/m+n)  

(oh i remember its section formula)

x=5a+2a*2/a+2a

x=9a/3a

x=3

and

y=-8a+2a*1/a+2a

y=6a/2a

y=3

substituting x and y values in 2x-y+k=0

(as P lies on the line )

2(3)-3+k=0

k=3

HOPE IT HELPS