Segment AB is given with midpoint m. Also, c is a point between A and M. Prove, cm=(1/2)(CB-CA)

Question

Segment AB is given with midpoint m. Also, c is a point between A and M. Prove, cm=(1/2)(CB-CA)

Answer 1

 

  well ,  AB = CB + CA   by distance postulate

 

So

           AB - CA = CB    <--- subtracts CA from both sides

and

           AB - 2*CA = CB - CA  <--- subtracts CA from both sides again!!!

 

 

multiplying both sides by 1/2:

    (1/2) (AB) - CA = (1/2)(CB - CA)

 

     AM  - CA   = (1/2)(CB - CA) <---- M is the midpoint, so AM = (1/2)(AB)

 

    CM = (1/2)(CB - CA)  <---- since c is between A and M, AC + CM = AM, so CM = AM - AC = AM - CA

 

end of proof