Point 1 (x₁, y₁)
x₁
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y₁
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Point 2 (x₂, y₂)
x₂
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y₂
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Quick Examples
Midpoint
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Sources & Methodology
Midpoint formula verified against Khan Academy coordinate geometry curriculum and the National Council of Teachers of Mathematics (NCTM) standards.
Khan Academy — Midpoint Formula Review
Standard curriculum reference for the midpoint formula, coordinate geometry applications, and verification methods used in this calculator
NCTM — Principles and Standards: Geometry
Authoritative mathematics education standards defining coordinate geometry skills including midpoint and distance in the plane
Methodology: Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2). Coordinates are averaged independently. Distance from each point to midpoint is computed using the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) / 2. Verification: both distances must equal half the total segment length.
⏱ Last reviewed: April 2026
How to Find the Midpoint Between Two Points
The midpoint is the point that lies exactly halfway between two coordinate points on a plane. It is equidistant from both endpoints and sits at the centre of the line segment connecting them. The midpoint formula averages the x-coordinates and averages the y-coordinates independently.
The Midpoint Formula
M = ( (x₁ + x₂) / 2 , (y₁ + y₂) / 2 )
Where (x₁, y₁) and (x₂, y₂) are the two endpoints.
Mx = average of x-coordinates My = average of y-coordinates
Example: midpoint of (2, 4) and (8, 10):
Mx = (2 + 8) / 2 = 5 My = (4 + 10) / 2 = 7 Midpoint = (5, 7)
Mx = average of x-coordinates My = average of y-coordinates
Example: midpoint of (2, 4) and (8, 10):
Mx = (2 + 8) / 2 = 5 My = (4 + 10) / 2 = 7 Midpoint = (5, 7)
Worked Examples
| Point 1 | Point 2 | Mx = (x₁+x₂)/2 | My = (y₁+y₂)/2 | Midpoint |
|---|---|---|---|---|
| (0, 0) | (6, 8) | 3 | 4 | (3, 4) |
| (2, 4) | (8, 10) | 5 | 7 | (5, 7) |
| (-4, 2) | (2, -6) | -1 | -2 | (-1, -2) |
| (-3, -5) | (5, 7) | 1 | 1 | (1, 1) |
| (1, 3) | (7, 3) | 4 | 3 | (4, 3) |
Finding a Missing Endpoint
If you know one endpoint (x₁, y₁) and the midpoint (Mx, My), you can find the other endpoint by rearranging the formula: x₂ = 2×Mx − x₁ and y₂ = 2×My − y₁. For example, if endpoint is (1, 3) and midpoint is (4, 5): x₂ = 2×4 − 1 = 7, y₂ = 2×5 − 3 = 7. Missing endpoint: (7, 7).
Related Formula: Distance Between Two Points
d = √ ( (x₂ − x₁)² + (y₂ − y₁)² )
The distance formula gives the length of the segment. The midpoint lies at distance d/2 from each endpoint. Both formulas come from the Pythagorean theorem applied to the coordinate plane.
💡 Real-World Uses: GPS navigation uses midpoint calculations to find halfway points between locations. In construction, the midpoint bisects a wall or beam accurately. Computer graphics use midpoints for line drawing algorithms, bezier curves, and centre-finding. In data science, the midpoint of a range is used in histogram bin calculations and data normalization.
Frequently Asked Questions
The midpoint formula finds the exact centre point between two coordinate points. For points (x₁, y₁) and (x₂, y₂), the midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2). You average the x-coordinates to get Mx and average the y-coordinates to get My. The midpoint always lies on the line segment between the two original points.
Add the two x-coordinates and divide by 2 to get Mx. Add the two y-coordinates and divide by 2 to get My. Example: midpoint of (2, 4) and (8, 10) is ((2+8)/2, (4+10)/2) = (5, 7). The process is the same whether coordinates are positive, negative, whole numbers, or decimals.
A midpoint is the point that lies exactly halfway between two other points — equidistant from both. In coordinate geometry, the midpoint divides the line segment connecting two points into two equal halves. Any line that passes through the midpoint and is perpendicular to the segment is the perpendicular bisector of that segment.
Yes. If one or both original points have negative coordinates, the midpoint may also be negative. The formula works identically. Example: midpoint of (-4, 2) and (2, -6) is ((-4+2)/2, (2-6)/2) = (-1, -2). The sign is handled automatically by the arithmetic — no special treatment needed.
Rearrange the formula. If you know endpoint (x₁, y₁) and midpoint (Mx, My), then x₂ = 2×Mx − x₁ and y₂ = 2×My − y₁. Example: endpoint (1, 3), midpoint (4, 5) → x₂ = 8−1 = 7, y₂ = 10−3 = 7. Missing endpoint: (7, 7).
Midpoint calculations are used in GPS navigation to find halfway waypoints, construction to bisect structural elements, computer graphics for line drawing and shape centering, data analysis to find class midpoints in frequency tables, and sports analytics to find the centre of a playing field or trajectory path.
The midpoint formula M = ((x₁+x₂)/2, (y₁+y₂)/2) gives the coordinates of the centre point — a location. The distance formula d = √((x₂−x₁)² + (y₂−y₁)²) gives the length of the segment — a measurement. Both derive from the Pythagorean theorem but answer different questions.
Yes. In three dimensions, the midpoint of (x₁, y₁, z₁) and (x₂, y₂, z₂) is ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). The same averaging applies to each dimension. The principle extends to any number of dimensions, making it fundamental in higher-dimensional geometry and machine learning distance calculations.
Calculate the distance from each original point to your midpoint using the distance formula. Both distances must be equal. Each must also equal exactly half the total segment length. Alternatively, confirm the midpoint x-coordinate is between x₁ and x₂, and the midpoint y-coordinate is between y₁ and y₂ (or equal to them for horizontal/vertical segments).
If both points are identical, say (3, 5) and (3, 5), the midpoint is that same point (3, 5). This makes sense geometrically — a line segment of zero length has its midpoint at itself. The formula gives ((3+3)/2, (5+5)/2) = (3, 5), and the distance between the points is 0.
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