Math
Endpoint Calculator
Given one endpoint and the midpoint, mathcheck reverses the midpoint formula to find the other endpoint.
It also reports the full segment length, the distance from each endpoint to the midpoint, and the equation of the line through the points, and verifies the midpoint. Switch modes to find a midpoint from two endpoints.
x-coordinate of the endpoint you know.
y-coordinate of the endpoint you know.
Try an example
Result
Result
—
- Endpoint A
- —
- Endpoint B
- —
- Segment length
- —
- Endpoint to midpoint
- —
- Line through the points
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
The endpoint formula
The The point exactly halfway between two other points. is the average of the endpoints. If you know one endpoint and the midpoint, solve the midpoint formula for the unknown endpoint: double the midpoint and subtract the known endpoint, one coordinate at a time. Geometrically, the midpoint is exactly as far from the known endpoint as from the missing one, so you travel the same displacement again.
Endpoint (1, 2), midpoint (4, 6)
x2 = 2(4) - 1 = 7. y2 = 2(6) - 2 = 10. The missing endpoint is (7, 10). Check: ((1 + 7)/2, (2 + 10)/2) = (4, 6).
Need the midpoint instead?
Switch to Midpoint mode to average two endpoints, or use the dedicated midpoint calculator linked below for a graph and the distance between the points.
How to use this calculator
- Choose Missing endpoint or Midpoint.
- Enter the known endpoint, then the midpoint (or the second endpoint).
- Read the missing endpoint (or midpoint) as an ordered pair.
- Use the segment length and half-length if the problem asks how long the segment is.
- Open Show the work to see the doubled-midpoint subtraction and the check.
How to read the answer
The missing endpoint is the mirror image of the known endpoint across the midpoint, so it lies on the same line at the same distance on the other side. The segment length is twice the distance from either endpoint to the midpoint, and the line equation shows the line all three points share.
Common mistakes and edge cases
- Averaging the endpoint and midpoint, which gives a point only a quarter of the way along the segment.
- Forgetting to double the midpoint before subtracting.
- Subtracting in the wrong order: it is 2M - P, not P - 2M.
- Mixing up which point is the midpoint and which is the endpoint.
- If the midpoint equals the endpoint, the segment has zero length and the other endpoint is the same point.
Worked examples
Whole-number endpoint
Endpoint (1, 2), midpoint (4, 6)
Result
(7, 10)
Negative coordinates
Endpoint (-3, 5), midpoint (1, -2)
Result
(5, -9)
Decimal midpoint
Endpoint (2, 3), midpoint (3.5, 1.25)
Result
(5, -0.5)
Midpoint at the origin
Endpoint (4, -7), midpoint (0, 0)
Result
(-4, 7)
Midpoint mode
Endpoints (1, 2) and (7, 10)
Result
(4, 6)
Degenerate segment
Endpoint (3, 3) and midpoint (3, 3)
Result
(3, 3)
Frequently asked questions
How do I find the other endpoint when I know the midpoint?+
Double each midpoint coordinate and subtract the known endpoint: x2 = 2Mx - x1 and y2 = 2My - y1.
Why do I double the midpoint?+
Because the midpoint formula divides the sum of the endpoints by 2. Multiplying by 2 undoes that division, leaving x1 + x2, and subtracting x1 isolates x2.
Can the missing endpoint have negative coordinates?+
Yes. If the midpoint is closer to the origin than the known endpoint, the other endpoint often lands on the opposite side with negative coordinates.
How is the segment length related to the midpoint?+
The midpoint splits the segment into two equal halves, so the full length is twice the distance from either endpoint to the midpoint.
Does this work in 3D?+
The same idea works with a z-coordinate: z2 = 2Mz - z1. This page handles 2D; use the 3D distance calculator for three-dimensional midpoints.
How do I check my answer?+
Average the known endpoint and your answer. If you get the given midpoint back, the endpoint is correct. The calculator shows this check in the work.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Midpoint Calculator
Find the midpoint between two coordinate points with coordinate-average steps.
Distance Formula Calculator
Find the distance between two coordinate points with dx, dy, squared distance, and square-root steps.
Slope Calculator
Find slope from two points, solve a missing coordinate from a known slope, or turn an angle or percentage grade into a slope. Includes equations, intercepts, perpendicular slope, graph, and step-by-step work.
Perpendicular Line Calculator
Find the equation of the line perpendicular to a given line through a point using the negative reciprocal slope. Accepts any line form, graphs both lines, and shows where they meet at a right angle.
3D Distance Calculator
Find the distance between two points in 3D space with the exact radical form and decimal, plus the midpoint, the direction vector from P to Q, its unit vector, and direction angles.
Slope Intercept Form Calculator
Write the equation of a line in slope-intercept form y = mx + b from two points, a point and a slope, or standard form. Exact fractions, intercepts, a graph, and every other form of the line.
Last updated: September 4, 2026