This online Midpoint Calculator finds the midpoint of a line segment in the two-dimensional plane. You have to specify the coordinates (x1,y1) and (x2,y2) of the first and second points of the line segment. After clicking the Calculate button you will get the coordinates (xm,ym) of the midpoint and the graph of the line segment and the points.
How to Find Midpoint of a Line Segment
The midpoint of a line segment is a point that lies halfway between the two endpoints of the line segment. In other words, the middle point is the same distance from each end point.
For a line segment with endpoints \((x_1,y_1)\) and \((x_2,y_2)\) the midpoint is located at the point with Cartesian coordinates:
$$x_m = \frac{x_1+x_2}{2}, \ y_m = \frac{y_1+y_2}{2},$$
or using the midpoint formula:
$$(x_m,y_m) = \left ( \frac{x_1+x_2}{2}, \ \frac{y_1+y_2}{2} \right ).$$
By plugging in the coordinates of the endpoints into our Midpoint Calculator, you can easily get the coordinates of the midpoint as well as the graph of the line segment and its endpoints.
The midpoint formula is often used in solving everyday problems, and is also used in various fields of science, technology and economics.
For example, if you need to get from one city to another and you want to split the driving into two days, you need to find a “midpoint” (i.e. a city roughly in the middle between the two cities). The easiest, though not ideal, way is to use the midpoint formula, provided you know the coordinates of the cities.
And here’s a more relevant example. Imagine an airplane flying between two cities gets some engine damage. In this case, the pilots need to determine from the GPS coordinates whether the aircraft is less than half the distance to its destination or not. Only then can the decision be made to either turn back or continue flying to the final destination. The calculation of distances is programmed into the on-board navigation systems.
The midpoint formula is used in economics to find the coefficient of elasticity of demand and supply in various models. The price elasticity of demand, for example, is the responsiveness of the quantity demanded to a change in the price. It is defined as the percentage change in quantity demanded divided by the percentage change in price. The elasticity is usually calculated using the average percentage change in both quantity and price. In this case, the change in the value of the quantity is divided by the value of the midpoint between the initial and final values of this quantity. This is called the midpoint method for elasticity.
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Check out our other math calculators such as Perpendicular Line Calculator or Polar Coordinates Calculator.