We present an approach to two-body collision processes which simplifie
s the algebra and leads to a convenient geometrical visualization of t
hese processes in the velocity plane. Special cases, such as the lab a
nd center-of-mass frames, can easily be extracted from the general sol
utions without further algebra. The geometric interpretation provides
insight into the dynamics of collisions without having to consider num
erous special cases, Thus important physics concepts can be illustrate
d without students becoming lost in the algebra. (C) 1997 American Ass
ociation of Physics Teachers.