Hey, there!

1. Think about a seesaw. 

A_______________|________________B.

                center

We put weights on A and B, so that they may balance. If the center point is the middle, I should put the same weights on A and B so that it may balance.

Let's say the distance between A and B is 10. I have a coordinate of A as 0 and that of B as 10. The midpoint is 5.

I put the same weight on A and B as 1 kg and 1 kg respectively. Then, the distance from the center to A and that to B are actually same. 

Here is what we do, using weights.

I contribute the amount of weights 1 kg out of 2 kg(in total) to A, and 1 kg out of 2 kg (in total) to B.

In fact, 1/2 (0) + 1/2 (10) = 5.

This is how we use interior points!

If I explain it differently, consider it this way.

A(0) ____________Midpoint(x)_____________B(10)

The distance from the midpoint to A equals the distance from B to the midpoint, i.e, 

x - 0 = 10 - x

Hence, 2x = 10, so x=5.

This might be a better tool in terms of labeling and setting up ratio/expression.

2. Your understanding is excellent. You choose the first point in 6 ways, then the second point must be 3 points, not 5 points, IF WE WERE LOOKING FOR diagonals. Otherwise, it would have been 5 ways for the second point.

Yay!!