Connecting anchor points on closed paths

All of these work, so take your pick!

Draw line segment (or whatever shape) across path you want to divide.

Select both paths.

Select Live Paint Bucket

Choose color you want from Swatches panel

Click in area you want to change.

Peter

One technique would be to use the Scissors tool to click on the two points to cut the path.

This will result in two separate open paths. You can fill each with a different color.

If you need a stroke connecting the two, just Object > Path > Join to make each into a closed path.

There are many ways to achieve this, one of the way is as follow -

1. Create a line from one end to another end.. like this -

2. Select both the line & end the object with fill, than go to the Pathfinder and choose divide -

3. step 2 will create two closed paths/shapes and group them, double click on the shape to change color or ungroup it to change color of closed paths/shapes -