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Midpoint Formula Examples

In geometry, the midpoint formula is used to find the coordinates of the midpoint of a line segment between two points in the Euclidean plane.

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Video Transcript

Okay, so we're here to talk about or look at some examples regarding the midpoint formula. So recall that the mid port midpoint formula is the average of your exes comma, the average of your wise given any two points. X one y one and x two y two. So there's basically two questions could be asked two basic questions, and then we can do some contextual problems. So the very first question would be, Hey, given the points 3 11 and negative. Eight. Comma two. How about Cama three. What's the midpoint? Well, the midpoint is gonna be again. The average of your excess cama. The average of your wise well three minus eight is negative fives you love with negative five halves. Leave it like that. 11 plus three is 14 and then over to is seven. So there you go. There's a midpoint. Simple is that just finding the average of the X is an average. Otherwise, in fact, I find it easier to think of. The mid point is it's the average of accent wise and not actually think of the formula because it makes more sense conceptually. Okay, here's another example. Let's suppose you're given an end point, and it's too common negative. Seven. You're given the midpoint, which is five. Comma. I'll say Negative 10. And I wanna know what's the other end point. We do this two ways. One is we know that the midpoint is found by the averaging of two X and two y's. So it would be like saying two plus something over two equals five and negative seven plus something over to equals. Negative. 10. Okay, this would be to plus X equals 10. Or, in other words, X equals eight. This would be negative. Seven plus y equals negative 20. Or, in other words, why equals negative 13. And so you know your other end point would be eight. Common negative. 13. This is essentially using the midpoint formula backwards. We're setting the average equal to the known average, and we just have to, you know, be looking for what would get us the average to be five or negative 10. There's another way to look at this. I want you to think that if you go from end point to midpoint, there's some over and up that you must go well to get to your other end. point, you must go over the same and up the same since the slope has to be the same, it to be consistent. So here's what. Here's what you can think of what happened between two and five. We went up by three. So do it again. What's five plus three eight? Okay. What happened between negative seven and negative 10. We actually subtracted three. We went three lower. Okay, subtract three. Look at that. You could skip all of the algebra if you just look at the pattern of how far up or down we're left or right, you go depending on what you're looking at, and you can get your other end point. Okay, So what is the other questions you could see here? They might say something like, you know, a circle a circle. And they tell you about its diameter. Here's what we know about its diameter. The diameter has endpoints at let's say 24 and negative 37 The question is, what's the area of the circle? Well, to find the area of the circle, we need to find the radius. But in order to find the radius, we need to find the diameter So, um, what we could do is two things. One is we could find the distance between these two points that would give us the length of the diameter. Divide that by two. Then we could do pi r squared, and then we would have our area of the circle. Or we could say, Even before then, I guess I could have asked this question. Here's a circle. Here's the diameter with endpoints. What's the center of the circle? Let me ask that question first, what's the center of the circle? So let me get rid of this. Get ahead of myself here. So if I said here's a circle diameter with end points at 24 and negative 37 where is our center located? This is basically find the midpoint. All right, that will be two plus negative. 3/2 comma, four plus seven over two, and it's going to get you he center of negative one half comma. 11 half's. Okay, then, if you wanted to, you could extend yourself by finding, you know, let's say the extension questions where Let's find the area. Let's find the circumference. Either way, we need to find the radius So you you need to find the distance between the endpoints, find length of diameter, cut it in half, and then you can use pi r squared or two pi r. So I got ahead of myself a little bit, but this could be an example of how to find why we would use my point. Okay, I'll see you next time.