Sexing koi isnt an exact science, all one needs to do is turn over a mature 10" koi to sex them.
When sexing koi there are a number of tell tale signs:
1) A female koi's fins are more rounded
2) A male koi's fins are more pointed
3) A females body is larger and more rounded
4) A male koi's body is far thinner
To sex a female: When you look at the vent area you should be seeing that a female koi has a line running from head to tail which has another line running across the bottom of it. Imagine the koi running head to tale left to right on the page, the vent area of a female will look very similar to this.
To sex a male: Males do not have this cross piece at the bottom just a simple line running hed to tail, a male is also thinner than a female and its pectorals are far rounder again running head to tail left to right a males vent area will look like this --