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

given

ap/pb = 1/3

If p divides internally

m = 1, n = 3

coordinates of p

= (5*1 + 2*3)/(1+3), (-8*1 + 1*3)/(1+3)

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

= 11/4, -5/4

since this point lies on 2x - y + k = 0

2*(11/4) - (-5/4) + k = 0

17/4 + k = 0

k = -17/4

2. If p divides externally

m= 1, n = 3

coordinates of P

= (5*1 - 3*2)/(1-3), (-8*1 - 3*1)/(1-3)

= (5 - 6)(-1), (-8 -3)/(-1)

= 1, 11

if this point lies on 2x - y + k = 0

2*1 - 11 + k = 0

k = 9