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Midpoint Formula Derivation

In mathematics, the midpoint formula is a formula for the coordinates of the midpoint of a line segment between two points with Cartesian coordinates (x1, y1) and (x2, y2).


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Video Transcript

Okay. Hey, guys. We're back today to talk about the midpoint formula, Another very super duper common formula that you see along with the distance formula and things that fall under the category of coordinate geometry. So the midpoint formula is exactly what it says. It's a formula to help us figure out the midpoint of a given line segment. Okay, so suppose you have again on the coordinate grid to random points. I'm gonna call this point A and its coordinates are X one comma Y one, and then I have some other point b. I'm gonna call its coordinates X two comma. Why to Well, I'm looking for the midpoint of this segment, which is gonna be somewhere in here. And I want you to think that the midpoint is in the middle of both your X coordinates and your white coordinates. Its's in the middle of this distance, but it's also in the middle of this distance. So if you think about how do you find the middle of two values That's really the average. So to find the x coordinate of this midpoint, I'm gonna take my two X coordinates individually, and I'm gonna find their average. Likewise, we do the same with the Y coordinates, and that is your mid port midpoint formula. It's literally just the average of your X and Y coordinates, respectively. I'll be back later with more examples.