The midpoint formula averages the x-coordinates and y-coordinates separately. For two points (x1, y1) and (x2, y2), the midpoint M is the arithmetic mean of each coordinate pair. Three formulas work together to fully describe the relationship between two points.
The distance formula comes from the Pythagorean theorem: the horizontal difference is one leg, the vertical difference is the other, and the segment is the hypotenuse. Slope measures vertical change per unit of horizontal change. To find values between two known data points (a related concept), see the Linear Interpolation Calculator.
The midpoint and distance formulas are used together across coordinate geometry. Midpoint finds the center of a segment; distance finds its length. The table below shows when to use each.
| Task | Formula | Result | Application |
|---|---|---|---|
| Find center of segment | Midpoint | M = ((x1+x2)/2, (y1+y2)/2) | Bisect a line, find midpoint of map route |
| Find segment length | Distance | d = sqrt((dx)^2 + (dy)^2) | Measure straight-line distance |
| Find perpendicular bisector | Midpoint + slope | Use midpoint and slope = -1/m | Construct perpendicular bisector |
| Find missing endpoint | Midpoint reverse | x2 = 2mx - x1 | Locate other endpoint from midpoint |
Finding the missing endpoint is a common geometry problem: if you know midpoint M and one endpoint A, solve for the other endpoint B. This calculator computes midpoint forward (given two endpoints); to find a missing endpoint, use the reverse formula x2 = 2mx - x1. For statistical applications that involve coordinate-style data, see the Correlation Coefficient Calculator.
In economics, the midpoint formula (also called arc elasticity) calculates price elasticity of demand using the average of two price and quantity values as the base, rather than the starting value. This prevents the elasticity from changing based on direction of the price change.
The economic midpoint method uses the same averaging principle as the geometric midpoint: (Q1+Q2)/2 is literally the midpoint between the two quantity values. This ensures symmetric results. For economic data summary statistics, see the Mean Median Mode Calculator.
Geometry homework: find the midpoint, distance, and slope between A(-3, 5) and B(7, -1).