Question

If p(9a-2,-b) divided the line segment joing a(3a+1,-3) and b(8a,5) in the ratio 3:1, find the values of and b

Answer 1

a-----------------------p-------------------------------b
[3a+1,-3]           [9a-2,-b]                           [8a,5]
 
according  to section formula 

=[{24a+3a+1}/4 , {15-3}/4]
=[(27a+1)/4  ,12/4]
=[(27a+1)/4 ,3]

so comparing to given p[9a-2,-b]
9a-2=[27a+1]/4
36a-8=27a+1
9a=9
a=1

and also -b=3
=>b=3