Midpoint Calculator
Find the midpoint between two points, calculate distance, slope, and line equation. Supports endpoint finding, section formula, and 3D coordinates.
Results
Midpoint
(5.0000, 5.0000)
Input
Point 1 (x1, y1)
Point 2 (x2, y2)
Coordinate Plane
Complete Results
Midpoint
(5.0000, 5.0000)
Distance
7.2111
Line Properties
Slope (m)
0.6667
Angle
33.69deg
Perpendicular Slope
-1.5000
Y-Intercept
1.6667
Line Equations
Slope-Intercept Form
y = 0.6667x + 1.6667
Standard Form
-0.6667x + 1y = 1.6667
Coordinate Geometry Formulas
Midpoint & Distance
- M = ((x1+x2)/2, (y1+y2)/2)
- d = sqrt((x2-x1)^2+(y2-y1)^2)
- Endpoint = (2Mx-x1, 2My-y1)
Slope & Line
- m = (y2-y1)/(x2-x1)
- y = mx + b
- Perpendicular: m' = -1/m
Section Formula
- Internal: ((mx2+nx1)/(m+n),
- (my2+ny1)/(m+n))
- Midpoint: m=n=1
3D Formulas
- M = ((x1+x2)/2, (y1+y2)/2,
- (z1+z2)/2)
- d = sqrt(dx^2+dy^2+dz^2)
Results
Midpoint
(5.00, 5.00)
Coordinate Geometry Examples
Quick-start with common scenarios
Practice Coordinate Geometry
Test your skills with practice problems
Practice with 4 problems to test your understanding.
?How to Calculate Midpoint and Related Values
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). Distance formula: d = sqrt((x2-x1)^2 + (y2-y1)^2). Slope formula: m = (y2 - y1)/(x2 - x1). To find an endpoint when given midpoint and one point: endpoint = (2*midpoint - known point). Section formula divides a line in ratio m:n: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)).
What is a Midpoint?
The midpoint of a line segment is the point that divides the segment into two equal parts. It is located exactly halfway between the two endpoints. The midpoint formula averages the coordinates: M = ((x1+x2)/2, (y1+y2)/2). The section formula generalizes this to divide a segment in any ratio m:n, where the midpoint is the special case where m=n=1.
Key Facts About Coordinate Geometry
- Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
- Distance = sqrt((x2-x1)^2 + (y2-y1)^2)
- Slope (m) = (y2 - y1)/(x2 - x1) = rise/run
- Perpendicular slope = -1/m (negative reciprocal)
- Line equation: y - y1 = m(x - x1) or y = mx + b
- Section formula: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n))
- Internal division: point lies between the two endpoints
- External division: point lies outside the segment
- 3D midpoint: M = ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)
- 3D distance: d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
Quick Answer
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). Distance formula: d = sqrt((x2-x1)^2 + (y2-y1)^2). Slope formula: m = (y2 - y1)/(x2 - x1). To find an endpoint when given midpoint and one point: endpoint = (2*midpoint - known point). Section formula divides a line in ratio m:n: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)).
Frequently Asked Questions
Use the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). Simply average the x-coordinates and average the y-coordinates. For example, the midpoint of (2, 4) and (6, 8) is ((2+6)/2, (4+8)/2) = (4, 6).
The distance between two points is d = sqrt((x2-x1)^2 + (y2-y1)^2). This comes from the Pythagorean theorem. For points (0,0) and (3,4): d = sqrt(9+16) = sqrt(25) = 5.
If you know one endpoint (x1, y1) and the midpoint (Mx, My), the other endpoint is (2*Mx - x1, 2*My - y1). For example, if midpoint is (5, 7) and one point is (3, 4), the other point is (2*5-3, 2*7-4) = (7, 10).
The section formula finds a point that divides a line segment in a given ratio m:n. For internal division: P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n)). The midpoint is the special case where m = n = 1.
Slope (m) = (y2 - y1)/(x2 - x1) = rise/run. It measures the steepness of a line. Positive slope goes up-right, negative slope goes down-right. A vertical line has undefined slope, a horizontal line has slope 0.
The perpendicular slope is the negative reciprocal of the original slope: m_perp = -1/m. If a line has slope 2, perpendicular lines have slope -1/2. Exception: horizontal and vertical lines are perpendicular (slopes 0 and undefined).
Last updated: 2026-01-15
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
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Results
Midpoint
(5.0000, 5.0000)