How do you find the midpoint between two points?

 
Relevant MM Lessons:

Overview: The Midpoint Formula

This question has its own dedicated lesson ». Make sure to check it out if you need a more thorough read, or want to become an expert on how the Midpoint Formula shows up on tests.Given any two coordinate points in the plane, we can find the point directly between them. When we're asked to do this, we could inspect to find the answer visually, but we should be able to rely on a systematic algebraic approach.The formula for the midpoint between two points, $(x_1, y_1)$ and $(x_2, y_2)$ is:$$\mathrm{MP} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$For some reason, when I was first taught this, I couldn't remember it for the life of me. A short while later, someone told me that it's simply representative of the average $x$ coordinate and the average $y$ coordinate, and it never left me since. This is the way I would recommend "memorizing" it.We can see this in action with a quick example. Let's say we are asked to find the midpoint between $(3,10)$ and $(11,4)$.We could blindly use the formula verbatim, and we will of course get the right answer, but let's instead think more conceptually in a way that we'll never forget. The midpoint will be the average $x$ coordinate and the average $y$ coordinate. The average of $3$ and $11$ is $7$. The average of $10$ and $4$ is also $7$. Therefore, the midpoint between $(3,10)$ and $(11,4)$ is $(7,7)$.And we can see from the picture that this makes sense visually as well.