What is the midpoint equation?


Quick Answer

The midpoint equation finds the midpoint of a line segment between two points. For two points A and B with x and y coordinates (x1, y1) and (x2, y2), the midpoint M is ((x1+x2)/2, (y1+y2)/2).

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Full Answer

The midpoint also applies to a three-dimensional geometry. If line segment AB is formed by connecting the points A = (x1, y1, z1) and B = (x2, y2, z2), the midpoint M is ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2). Geometrically, the midpoint can be found by drawing two circles and two lines. One circle is centered at A with the arc going through B, while the other circle is centered at B with the arc going through A. One line is drawn between the two circle intersection points, while the other line is drawn between points A and B. The intersection point of the two lines is the midpoint.

For example, to find the midpoint between the points (4, 9) and (6, 3), the equation requires adding 4 and 6 for a sum of 10 and then dividing this sum by 2 for the x-coordinate point of the midpoint, which is 5. Similarly, the y-coordinate point of the midpoint is found by adding 9 and 3 for a sum of 12, and then dividing 12 by 2, yielding a y-coordinate midpoint of 6.

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