People calculate midpoints both real life and in math class. For example, you may need to figure the midpoint if you are taking a long trip. The midpoint may be the place where you would like to stop and rest before continuing your journey. For more complex mathematical calculations, sometimes the midpoint is needed for constructing models or calculating distances and locations between objects. Because it is in the middle and each side of the line segment is equal, that information may be used in mathematical proofs of theorems.
To better understand midpoints, simply think of them as averages. Because bisecting a segment divides it into two equal halves, it is like getting the average. For example, if you have a line segment on a number line that runs between 5 and 10, all you have to do to find the number that is halfway between those two numbers is to add them and divide by two. This is the same way you would get an average. Five plus 10 is 15, and 15 divided by 2 is 7.5, so that is the midpoint. If you do not have a number line but only have two points, you would need to measure the distance between them and divide by two to get the midpoint.
There may be times when you need to get the coordinates of a midpoint of something other than a single straight line. For example, on a graph you have a horizontal x-axis and a vertical y-axis, and each of those axes have coordinates. Coordinates of a point have the x-coordinate first and the y-coordinate second. To get the coordinates of the midpoint mathematically, use the midpoint formula: Add the x-coordinates of each point and divide by two to get the x-coordinate of the midpoint. Do the same to the two y-coordinates. For example, suppose the two points are (-2, 4) and (6, -10). Calculate -2 + 6 = 4; 4 divided by 2 is 2, so the x-coordinate is 2. For the y-coordinates, 4 + -10 = -6; -6 divided by 2 = -3, so the y-coordinate is -3. The midpoint is (2, -3).
Sometimes in more advanced math, it is necessary to find the equation for a line that is the perpendicular bisector of the line segment. This means it is not only cutting the line into two equal parts at the midpoint, but it also makes right angles at that point. Once you have found the midpoint, all you have to do to come up with the equation of the perpendicular bisector is figure out the slope. The slope is like the steepness or the slant of the line.
To determine the slope of a line that will be perpendicular, you calculate the slope of the original segment and then take the negative reciprocal of it. All that means is that you change the sign (from negative to positive or vice versa), change it to a fraction and invert it. Slope is represented as a fraction, and the top is the change in the y-coordinates while the bottom is the change in the x-coordinates. You just have to start with the same point each time. The slope for the previous segment would be -10 - 4 over 6 - (-2). That would be -14/8 or simplified to -7/4. The slope of the line that is perpendicular would have the slope of 8/14, or simplified to 4/7.