The rule of thumb you can use to make this intuitive: A change in velocity at a certain point x on an orbit will change the entire orbit, except that orbit wil

The rule of thumb you can use to make this intuitive: A change in velocity at a certain point x on an orbit will change the entire orbit, except that orbit will still continue to go through that one point x. So slowing down at perigee will not alter the perigee. (It is actually the most delta-v efficient way to lower the apogee.)