 Let us look at the midpoint formula given two points piece of one and piece of two given by the coordinates x of one y sub one and x of two y sub two The distance between them is given by the following formula now Let us first look at two examples and then go back to the derivation of this formula Find the point between one two and one seven So suppose this is one here So the point one two would be about here one two and then let's say point Seven is right there This is the point one seven one seven One two now we know that the midpoint of this line segment Must lie here so the X the x coordinate must be one What about the y coordinate? Well, it lies between two one seven and this is just the average the arithmetic mean of Seven and two seven plus two seven plus two is nine nine over two is just Four and a half four point five. So this would be four Four point five and yes two plus two point five Lance you there on four point five plus two point five Lance you at the point of one seven. So we're right in the middle. We found the midpoint Let us look at a second case Let us fix now the Y Coordinate so if we are at the point negative one four, let's say it is somewhere here if this is negative one and this is four and The point five four, let's say five four is around here the point five or So the midpoint of that line segment was like right in here So the y coordinate must be why we fixed it at the beginning And then what about the x coordinate where the x coordinate is just the arithmetic mean the average of five and negative one five Plus negative one Over two that is four over two, which is just two so this point must be the point two Four and again negative one plus three Lance you there and two plus three lance you at the point five four great So now let's use this to derive a formula for the general case if we have Two points Say this is piece of one. This is x sub one Y sub one and then the point piece of two which is given by a coordinate x sub two y sub two Then how can we find the coordinates of the midpoint? well The coordinates of that midpoint is Just going to be look at the x coordinate. It's going it's going from x sub one to x sub two It's going from x sub one to x sub two So this is just the average the arithmetic mean of those two quantities and The same applies to y y is going from y sub one to y sub two So we just take the arithmetic mean the average of those two quantities and that's it Thank you