 In this video, I'm going to talk about the midpoint formula and go through a couple of examples that uses the midpoint formula The first example that I'm going to do is just a simple, okay, find the midpoint between two coordinates example and the second one that I have over here is Actually, you know what one quartet is and you know what the midpoint is But you want to find what the other quartet is so this one over here is a little bit more difficult But we'll start with the easy stuff and then move over to the harder examples All right. So the first thing I'm actually going to write down is the the midpoint formula Right off the bat. So usually when we do midpoint formula, we write big M equals parentheses X1 plus x2 over Two okay, so this is x sub 1 what I mean by sub We write a 1 or a 2 below. It's not an exponent. A lot of students get that get that wrong. It's not an exponent It's just a label. It's basically what this means is this is the first x. This is the second x That's all that really means. Anyway, so you take your x's add them together divide by two and then also same thing for the y take y1 plus y2 and You divide by two add them together divide by two now There's another thing in math that you use if you take two numbers divide by two. That's also known as the average So during this during this video. I'm gonna say that a lot the average of the x's right here and the average of the y's That's what's used to find the midpoint. Okay, so this doesn't look like a normal formula that we that we've used in the past We have parentheses. We got commas and all sorts of stuff like that Basically what this is is we got a formula right here to find out what the x coordinate is and we got a formula right here to Find out what the y coordinate is that's what we use to find midpoint So that's why it looks a little bit different from the rest of them. Anyway, all right So what we want to do is we want to find the coordinates of the midpoint of Segment pq with n points p is negative eight three and q is negative two seven Okay, so what I want to do is I just want to use the midpoint formula here So my midpoint again, we usually say that a midpoint is m a little mistake that I made here Actually shouldn't do that. It's not m equals. It's simply just m midpoint Okay, you could probably put equals there, but it doesn't make much of a difference But anyway, I won't put an equal sign there m. So I want to take my x coordinates Add them together divide by two take the average of the x's and what I want to do is I want to take the average of the y's Okay, so now what I need to do is I need to take these numbers negative eight three and negative two seven and plug them Into the right spot now. This is where it gets a little bit tricky Make sure that you plug the x's in where they're supposed to go and the y's in where they're supposed to go Just don't mix them up So for p we have an x of negative eight and for q we have a negative two So for my midpoint, it's going to be negative eight plus and negative two divided by two And for the y's I have a y of three and a y of seven So we're gonna have three plus seven divided by two just getting just the average of the numbers All right, so eight I'm gonna do this all at once negative eight plus negative two two negative numbers We're gonna add to get a bigger bigger negative number. So this is negative ten divided by two is negative five So I know what the x coordinates Of my midpoint is it is negative five and then over here three plus seven divided by two Three plus seven is ten ten divided by two is five. Okay positive five So my midpoint is negative five five. So that's the point that's halfway in between these two coordinates All right, so again, that's using the midpoint formula pretty simple. Just make sure you plug in the points where they're supposed to go all right, so Now let's do this next problem This one's a little bit more difficult the difficulty level between the first and the second problem here is is pretty steep Okay, so stick with me here m is the midpoint m is the midpoint of the segment x y So m is in the middle x has a coordinates of two seven case We're just like last time and m has a coordinates of six one. Okay, so this is where it's a little bit different We know what x is it's two seven and we know that the point in the middle is going to be six one It's a little bit different find the coordinates of y so now we're finding the coordinates on the outside So it kind of looks like this if you don't have a grid you don't have a graph with you Okay, so here's x here's m here's y we know that X is two seven. This is a very bad drawing. This is not very accurate drawing, but it gives us Kind of an example of what's going on. So x is two seven m is six one, but we don't know We don't know bad Question marks there. We don't know what y is so that's what we're here to find out Okay, alright, so we know where the middle is we know what the first point is we need to find the second point Okay Now what we're going to do is even though this problem is a lot different We're still going to use the midpoint formula just like the last problem We're still going to use the midpoint formula to start off. So my m is Eek not equal don't use the equal get rid of that is x1 plus x2 over 2 Y1 plus y2 over 2 Okay, now I'm going to plug in the things that I know I'm going to plug in the things that I know now This is where it's going to look a lot different from the previous problem but stick with me here now The thing is this part right here of m this middle point. We already know what that is We know it's six this piece right here We know that the coordinates of m are six one this piece We already know what the answer to is and we and x coordinate x coordinate those two We actually know what one of those already is if we look at our x coordinate Two so we actually know pieces here. So this is what it's going to look like when you solve these type of problems Two is one of the x's that we know the other x. We don't know That's one of these ones up here. We don't know okay So I'm just going to leave it as x2 divided by 2 but the thing is I know what the end results going to be So what I'm going to do is this piece is going to be equal to Six Now again, that looks very different from what we did over here But again, it's two different types of problems So again the formula looks the same that we're going to use but the method of solving is going to be a little bit different Okay, so to go over this once more M where do you know what the x coordinate is going to be it's going to be six So we know what the end results going to be and we know what one of the x coordinates is We know that it is two But we don't know what the other x coordinate is okay. That's why up here We don't know what that is so that is how that is why we set it up the way that we do okay Now the y portion over here in the second part is going to be set up the exact same way so now I know what one of the Y coordinates is it's seven Plus y2 Okay, I don't know what the other y-cord it is that's up over here I don't know what it is and divided by two and I know that eventually it's going to equal One I know eventually it's going to equal one So now what I have here is I actually have two equations that I need to solve To figure out what this x-cord it is and to figure out what this y-cord it is Okay, I got two equations to solve and both these equations are going to be two-step equations So I'm going to try to do all my work right here if I have space for it Okay, so now what I'm going to do with this portion of it If I want to solve for this variable here, I need to get rid of this to that's dividing So I need to multiply both sides by two. So 2x nope. Nope. Why am I using x? Don't use x 2 plus x sub 2 Equals 12 Multiply times 2 on both sides gets rid of the divide by 2 and then I got to multiply the 6 times 2 which is 12 And then get rid of this 2 over here. So I got to subtract it over x 2 is equal to 10 And we'll put my parentheses around that. I Don't necessarily need to put parentheses around that let's not do that save some space here okay So now that x 2 x sub 2 that tells me what the second x coordinate is supposed to be it's supposed to be 10 Okay, now I'm gonna come over here do the same thing get rid of this 2 to get rid of this 2 I got to multiply times 2 on both sides. Okay 7 plus y 2 Equals 2 if I multiply times 2 on this side It just gets rid of the divide by 2 if I multiply times 2 on this side 1 times 2 is going to be 2 Okay, take the 7 subtract it over to the other side y 2 is equal to this is 2 minus 7 is going to be a negative 5 All right, so now what I have here is I have what the second y coordinate is supposed to be I have what the second x coordinate is supposed to be and those represent this Point up here this y that's supposed to be on the edge So this tells me that my y coordinate is 10 negative 5 That's my answer Again the difficulty level of this type of problem is much higher than what the first one was over here I just keep that in mind with this you might have to wash that a couple of times to get all that The biggest struggle is to get from the first line here to the second because now we got these equals in here That's a little bit different. Okay, but you might have to watch this again to fully understand Fully understand what's going on All right, that is a couple of examples of the midpoint formula. Hopefully these will help Just make sure slow down take your time. Make sure you write out Make sure you write out the formulas to begin with so that you know where the numbers are supposed to go I just don't throw numbers in there willy-nilly You got to make sure I have some organizations this anyway. Hope these are a couple of examples out