How to Use Endpoint Calculator
The Endpoint Calculator reverses the midpoint formula to find the missing endpoint of a line segment. Enter the known start point and midpoint, select 2D or 3D mode, and the calculator returns the endpoint coordinates instantly.
- Select dimension – Choose 2D for planar problems or 3D for problems in three-dimensional space.
- Enter the start point A – Provide the known coordinates (x₁, y₁) or (x₁, y₁, z₁).
- Enter the midpoint M – Provide the midpoint coordinates (xₘ, yₘ) or (xₘ, yₘ, zₘ).
- Read endpoint B – The Endpoint Calculator shows the computed coordinates and the substitution steps.
This tool is particularly useful for coordinate geometry homework, proofs involving segment bisectors, and problems where you need to find a symmetric point about a given center.
Formula & Theory - Endpoint Calculator
The Endpoint Calculator uses the following derived formulas:
Given: A(x₁, y₁) and M(xₘ, yₘ) is the midpoint of AB
Then: x₂ = 2xₘ − x₁
y₂ = 2yₘ − y₁
In 3D: z₂ = 2zₘ − z₁| Symbol | Meaning |
|---|---|
| A(x₁, y₁) | Known start point |
| M(xₘ, yₘ) | Known midpoint |
| B(x₂, y₂) | Unknown endpoint to find |
| xₘ = (x₁+x₂)/2 | Midpoint formula, rearranged for x₂ |
| yₘ = (y₁+y₂)/2 | Midpoint formula, rearranged for y₂ |
The derivation is simple: since M is the midpoint, xₘ = (x₁ + x₂) / 2. Multiplying both sides by 2 and subtracting x₁ gives x₂ = 2xₘ − x₁.
Assumptions and Limits
The Endpoint Calculator accepts any real numbers for coordinates. For integer inputs, the result will always be an exact integer or half-integer, consistent with standard coordinate geometry. There are no restrictions on the range of input values.
Use Cases for Endpoint Calculator
The Endpoint Calculator is useful whenever you need to find a point that is symmetric to a known point about a given center. Common uses include:
- Coordinate geometry homework – Solve textbook problems that ask for the other endpoint of a segment given its midpoint.
- Geometry proofs – Locate symmetric points when constructing midpoint bisectors or median lines in triangles.
- Computer graphics – Find a reflected point across a center point in 2D or 3D design.
- Navigation and mapping – Determine an unknown waypoint when the start and midway positions are known.
- Physics and engineering – Find a position vector endpoint in 3D space for beam or truss analysis.
The Endpoint Calculator makes the reverse midpoint calculation transparent by showing the substituted formula for each coordinate, so you can learn the method and apply it independently to any similar problem.