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# Midpoint formula

CCSS.Math:

## Video transcript

let's say I have the point 3 comma negative 4 so that would be 1 2 3 and then down 4 1 2 3 4 so that's 3 comma negative 4 3 comma negative 4 and I also had the point 6 comma 1 so 1 2 3 4 5 6 comma 1 so just like that 6 comma 1 in the last video we figured out we could just use the Pythagorean theorem if we wanted to figure out the distance between these two points we just drew a triangle there and realize that this was the hypotenuse in this video we're going to try to figure out what is the coordinate of the point that is exactly halfway between this point and that point so this right here is kind of the distance the line that connects them now what is the coordinate of the point that is exactly exactly halfway in between the two what is this coordinate right here it's something comma something and to do that let me draw it really big here because I think are going to find out that it's actually pretty straight for it first it seems like a really tough problem G let me use the distance formula with some variables and you're going to see it's actually one of the the simplest things you'll learn in algebra and geometry so let's say that this is my triangle right there that is my triangle right there this right here is the point 6 comma 1 this down here is the point 3 comma negative 4 and we're looking for the point that is smack-dab in between those two points what are its coordinates it seems very hard at first but it's easy when you think about it in terms of just the X and the y coordinates what's this guy's x-coordinate going to be this out here this line out here represents X is equal to 6 this over here let me do it in a little darker color this over here represents X is equal to 6 this over here represents X is equal to 3 what will this guy's x-coordinate be well he's going to be smacked his x-coordinates going to be smack-dab in between the two x-coordinates right this is X is equal to 3 this is X equal to 6 he's going to be right in between this distance is going to be equal to that distance his X corn is going to be right in between the 3 and the so what do we call the number that's right in between the 3 and the 6 well we could we could even call that the midpoint or we could call it the mean or the average or however you want to talk about it we just want to know what's the average of 3 & 6 so to figure out this point the point halfway between 3 & 6 you literally just figure out 3 plus 6 over 2 which is equal to 4.5 so this x coordinate is going to be 4.5 let me draw that on this graph 1 2 3 4 point 5 and you see it's smack-dab in between that's its x-coordinate now by the exact same logic by the exact same logic this guy's y-coordinate is going to be smack-dab between y is equal to negative 4 and y is equal to 1 right so it's going to be right in between those so this is the X right there the y coordinate is just going to be right in between Y is equal to negative 4 and Y is equal to 1 so you just take the average 1 plus negative 4 over 2 that's equal to negative 3 over 2 negative 3 over 2 or you could say negative 1 point 5 negative 1 point 5 so you go down 1.5 it is literally right there so just like that you literally take the average of the X's take the average of the Y's or maybe I should say the mean to be a little bit more specific a mean of 22 points and you will get the midpoint of those two of those two points the point that's equidistant from both of them it's the midpoint of the line that connects them so the coordinates are 4 point 5 comma negative 1 point 5 let's do a couple more of these these actually you're going to find are very very straightforward but just to visualize it let me graph it let's say I have the point 4 negative 5 so 1 2 3 4 and then go down 5 1 2 3 4 5 so that's 4 negative 5 and I have the point 8 comma 2 so 1 2 3 4 5 6 7 8 comma 2 8 comma 2 so what is the coordinate of the midpoint of these two points the point that is Mac dab in between them well we just average the X's average the y so the midpoint is going to do the x-values or eight and four it's going to be 8 plus 4 over 2 and the y value is going to be well we have a 2 and a negative 5 so you get 2 plus negative 5 over 2 and what is this equal to this is 12 over 2 which is 6 comma 2 minus 5 is negative 3 negative 3 over 2 is negative 1.5 so that right there that right there is the midpoint is the midpoint you literally just average the X's and average the Y's or find their mean so let's graph it just to make sure it looks like the midpoint 6 negative 5 1 2 3 4 5 6 negative 1 point 5 negative 1 negative 1 point 5 yeah looks pretty good it looks like it's equidistant from this point and that point up there now that's all you have to remember average the extra take the mean of the X or find the X that's right in between the two average the Y's you've got the midpoint well I'm going to show you now is what's in many textbooks they'll write oh if I have the point x1 y1 and then I have the point actually I'll just stick in yellow it's kind of painful to switch colors all the time and then I have the point x2 y2 many books will give you something called the midpoint formula which once again I think is kind of silly to memorize just remember you just average find the X in between find the Y min between it's a midpoint formula formula what they'll really say is the midpoint so maybe we'll say the you know the midpoint X or maybe I call it cut it this way I'm just making up notation the X midpoint and the Y midpoint is going to be equal to and it'll give you this formula X 1 plus X 2 X 2 over 2 and then Y 1 plus y 2 over 2 and it looks like something you have to memorize but all you have to say is look that's just the that's just the the immediately average or the mean of these two numbers this is just the average or the mean of these two numbers the I'm just saying I'm adding them to the two together dividing by two adding these two together dividing by two and then I get the midpoint that's all the midpoint formula