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Midpoint Formula - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

When working with circle conic sections, we can derive the equation of a circle by using coordinates and the distance formula. The equation of a circle is (x - h) ^2 + (y - k)^2 = r^2 where r is equal to the radius, and the coordinates (x,y) are equal to the circle center. The variables h and k represent horizontal or vertical shifts in the circle graph.

The Midpoint Formula is a easy to use way to find the middle of two different points on a coordinate axis. So in this case, I have the point x1,y1. We don't know what the coordinates are but they, each have an x coordinate and y coordinate and the point x2,y2. The midpoint is going to be the point smacked up in the middle of those two. So somewhere in, for this particular problem, somewhere in here. Okay, it's not exact but it's going to be somewhere right in there.
How we actually end up finding it is just the average of the x values and the average of the y values. So the x values are going to be here and here our middle is just going to be right in the middle. So all we do is, average the x values, add them together, divide by 2 and do the same for the y's. Add the y's together, divide by 2. Now we're averaging something so order doesn't necessarily matter. We have 4+8, it's the same thing as 8+4 as long as we're adding them together adding the x's separately then the y's, everything should be fine. So that's how we find the midpoint of two points on the coordinate axis.

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