Endpoint Calculator
Find the missing endpoint of a line segment. Enter one known endpoint and the midpoint to see the answer, calculation steps and an interactive diagram.
Enter the known coordinates
Decimals and negative values accepted. Display rounded to 10 significant digits where needed.
Visual explanation
A → M → BContinue from A through M by the same distance to reach B.
Equal scale on both axes. The view centers on the midpoint.
B = (2mₓ − x₁, 2mᵧ − y₁)
Endpoint calculator: find the missing coordinates
This endpoint calculator finds the other end of a line segment when you know one endpoint and its midpoint. Enter the coordinates of A and M to calculate B. The result includes the endpoint formula, substitution steps and a diagram showing how the three points connect.
What is an endpoint?
An endpoint is a point at either end of a line segment. A segment has two endpoints, usually called A and B. Its midpoint, M, lies halfway between them, so the distances AM and MB are equal.
For example, if A is at 2 and the midpoint is at 5 on a number line, B must be at 8. You move 3 units from 2 to 5, then another 3 units from 5 to 8.
What is the endpoint formula?
Given the known endpoint A(x₁, y₁) and midpoint M(mₓ, mᵧ), the missing endpoint is:
B(x₂, y₂) = (2mₓ − x₁, 2mᵧ − y₁)
x₂ = 2mₓ − x₁
y₂ = 2mᵧ − y₁
Double each midpoint coordinate, then subtract the matching coordinate of the known endpoint. Keep the x-coordinates together and the y-coordinates together.
How to use the endpoint calculator
- Enter x₁ and y₁ for the known endpoint A.
- Enter mₓ and mᵧ for the midpoint M.
- Select Find endpoint to calculate B(x₂, y₂).
- Read the substitution steps and use the SVG diagram to see A, M and B.
Try the example buttons for positive, negative, vertical and horizontal cases. Reset returns to A(2, 4) and M(5, 7). Enter fractions as decimal values. Displayed results are rounded to 10 significant digits where needed; calculations use the entered numeric values.
How to find the missing endpoint: worked examples
Example 1: Positive coordinates
Known endpoint: A(2, 4). Midpoint: M(5, 7).
- x₂ = 2 × 5 − 2 = 8.
- y₂ = 2 × 7 − 4 = 10.
- The missing endpoint is B(8, 10).
Check the answer: ((2 + 8) / 2, (4 + 10) / 2) = (5, 7), which matches the given midpoint.
Example 2: Negative coordinates
Known endpoint: A(−6, 3). Midpoint: M(−1, −1).
x₂ = 2 × (−1) − (−6) = −2 + 6 = 4
y₂ = 2 × (−1) − 3 = −5
The missing endpoint is B(4, −5). Subtracting a negative value changes that subtraction to addition.
Example 3: Decimal coordinates
Known endpoint: A(1.5, −2). Midpoint: M(3.25, 0.5).
x₂ = 2 × 3.25 − 1.5 = 5
y₂ = 2 × 0.5 − (−2) = 3
The missing endpoint is B(5, 3).
Endpoint examples at a glance
| Case | Known A | Midpoint M | Missing B |
|---|---|---|---|
| Sloping | (2, 4) | (5, 7) | (8, 10) |
| Negative | (−6, 3) | (−1, −1) | (4, −5) |
| Vertical | (3, 2) | (3, 6) | (3, 10) |
| Horizontal | (−4, 2) | (1, 2) | (6, 2) |
| Same point | (2, 3) | (2, 3) | (2, 3) |
How the endpoint formula comes from the midpoint formula
The midpoint equation for x is mₓ = (x₁ + x₂) / 2. Multiply both sides by 2 to get 2mₓ = x₁ + x₂. Subtract x₁ from both sides to get x₂ = 2mₓ − x₁. Follow the same steps for y to obtain y₂ = 2mᵧ − y₁.
Another way to understand this is to continue the movement from A to M once more. The horizontal change is mₓ − x₁ and the vertical change is mᵧ − y₁. Adding those changes to M gives B.
Missing endpoint on a number line
For a known endpoint a and midpoint m, use b = 2m − a. If a = −4 and m = 3, then b = 2 × 3 − (−4) = 10. The midpoint 3 is 7 units from both −4 and 10.
Common mistakes to avoid
- Entering two endpoints: this tool needs one endpoint and a midpoint. If you know both endpoints, use the Midpoint Calculator.
- Doubling the wrong value: double the midpoint coordinate, then subtract the known endpoint coordinate.
- Mixing x and y: calculate each coordinate separately.
- Ignoring a negative sign: write negative values in parentheses to make subtraction clearer.
FAQ on Endpoint Calculator
Double each midpoint coordinate and subtract the corresponding coordinate of the known endpoint. If A(x₁, y₁) is known and M(mₓ, mᵧ) is the midpoint, then B = (2mₓ − x₁, 2mᵧ − y₁).
The endpoint formula is x₂ = 2mₓ − x₁ and y₂ = 2mᵧ − y₁, where A(x₁, y₁) is the known endpoint and M(mₓ, mᵧ) is the midpoint.
Yes. The endpoint formula works with negative numbers and decimals. For example, A(−6, 3) and M(−1, −1) give B(4, −5). Enter fractions as decimal values in this calculator.
Average the known endpoint and the calculated endpoint. Their midpoint should match the midpoint you entered: M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).