How do you find the missing endpoint of a line segment?

Use the midpoint formula rearranged: Endpoint2 = (2 × Midpoint) − Endpoint1. For example, if Endpoint1 is (2, 3) and the Midpoint is (5, 7), then Endpoint2 = (2×5−2, 2×7−3) = (8, 11).

What is the endpoint formula in coordinate geometry?

The endpoint formula is derived from the midpoint formula M = ((x1+x2)/2, (y1+y2)/2). Solving for the unknown endpoint gives: x2 = 2×Mx − x1 and y2 = 2×My − y1, where (Mx, My) is the midpoint and (x1, y1) is the known endpoint.

How do you find the endpoint when given the midpoint and one endpoint?

Multiply the midpoint coordinates by 2, then subtract the known endpoint coordinates. For x: x2 = 2×midpoint_x − x1. For y: y2 = 2×midpoint_y − y1. This works because the midpoint is the average of both endpoints.

Can you find the endpoint in 3D coordinates?

Yes. In three dimensions, apply the same formula to each axis separately: x2 = 2×Mx − x1, y2 = 2×My − y1, and z2 = 2×Mz − z1. The principle is identical — the midpoint is the average of corresponding coordinates.

What is the difference between endpoint and midpoint?

Endpoints are the two ends of a line segment. The midpoint is the exact center point that divides the segment into two equal halves. The midpoint is calculated by averaging the x-coordinates and y-coordinates of both endpoints.

Why do you multiply the midpoint by 2 to find the endpoint?

Because the midpoint formula averages the two endpoints: Midpoint = (Endpoint1 + Endpoint2) / 2. Multiplying both sides by 2 gives: 2 × Midpoint = Endpoint1 + Endpoint2. Subtracting the known endpoint isolates the unknown one.

How do I verify my endpoint calculation is correct?

Calculate the midpoint between your two endpoints using the midpoint formula. If M = ((x1+x2)/2, (y1+y2)/2) matches the given midpoint, your endpoint is correct. This verification is shown step-by-step in the results above.

What is the endpoint formula for a number line (1D)?

On a 1D number line, the formula simplifies to: Endpoint2 = 2 × Midpoint − Endpoint1. For example, if one endpoint is 3 and the midpoint is 8, then Endpoint2 = 2×8 − 3 = 13. The midpoint 8 is exactly halfway between 3 and 13.

Endpoint Calculator — CalculatorCove

Sources & Methodology

✓Formula verified against geometry curriculum standards from Khan Academy and NCTM Common Core standards for coordinate geometry.

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Khan Academy — Midpoint Formula

Foundation for the endpoint formula derivation — the midpoint as the average of both endpoints

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NCTM — Principles and Standards for School Mathematics

Coordinate geometry standards; finding missing coordinates given midpoints is a Grade 8–Geometry curriculum standard

Methodology: Given known endpoint (x₁, y₁) and midpoint (Mₐ, Mʏ), the missing endpoint is calculated as: x₂ = 2Mₐ − x₁ and y₂ = 2Mʏ − y₁. This is derived algebraically from the midpoint formula M = (x₁+x₂)/2, solved for x₂. The 3D extension applies the same logic to the z-axis. Results are verified by confirming the midpoint of the two endpoints matches the given midpoint.

⏱ Last reviewed: March 2026

How to Find the Missing Endpoint of a Line Segment

The endpoint calculator uses a key property of geometry: the midpoint of a line segment is the average of the two endpoints. When you know one endpoint and the midpoint, you can work backwards to find the second endpoint using the endpoint formula.

The Endpoint Formula

x₂ = 2Mₐ − x₁

y₂ = 2Mʏ − y₁

Where (x₁, y₁) is the known endpoint, (Mₐ, Mʏ) is the midpoint, and (x₂, y₂) is the missing endpoint.

Example: Known endpoint (2, 3), Midpoint (5, 7):
x₂ = 2×5 − 2 = 8 y₂ = 2×7 − 3 = 11 → Missing endpoint: (8, 11)

Why Does This Formula Work?

The midpoint formula states that M = (x₁ + x₂) / 2. Multiplying both sides by 2 gives 2M = x₁ + x₂. Subtracting x₁ from both sides yields x₂ = 2M − x₁. This is pure algebraic rearrangement — you are "undoing" the averaging that created the midpoint to recover the missing coordinate.

Worked Examples — Common Scenarios

Known Endpoint	Midpoint	Missing Endpoint	Verification
(0, 0)	(3, 4)	(6, 8)	Midpoint of (0,0)&(6,8) = (3, 4) ✓
(−2, 5)	(1, 3)	(4, 1)	Midpoint of (−2,5)&(4,1) = (1, 3) ✓
(7, −1)	(2, 4)	(−3, 9)	Midpoint of (7,−1)&(−3,9) = (2, 4) ✓
(0, 0, 0)	(2, 3, 5)	(4, 6, 10)	3D midpoint verified ✓
(1, 2, 3)	(4, 5, 6)	(7, 8, 9)	3D midpoint verified ✓

Finding Endpoints on a Number Line (1D)

On a 1D number line, the formula simplifies to a single equation: Endpoint2 = 2 × Midpoint − Endpoint1. For example, if one endpoint is at 3 and the midpoint is at 8, then the other endpoint is 2×8 − 3 = 13. You can verify: the midpoint of 3 and 13 is (3+13)/2 = 8.

Real-World Applications of the Endpoint Formula

Architecture & design: Finding the center point of a wall or beam, then working out where supports should be placed
Navigation: Knowing a starting point and the halfway point of a journey to find the destination
Computer graphics: Calculating endpoint coordinates for rendering line segments on screen
Physics: Finding the far end of a displacement vector when the center of mass is known
GIS & mapping: Locating the end of a route when the midpoint coordinate is given

💡 Pro Tip — Avoiding Common Mistakes: A frequent error is subtracting the midpoint from the known endpoint instead of multiplying. Remember: double the midpoint first, then subtract. The formula is x₂ = 2M−x₁, NOT x₂ = M−x₁. Using M−x₁ gives you the distance from the midpoint to the known endpoint, not the coordinate of the missing endpoint.

Frequently Asked Questions

Use the endpoint formula: Endpoint2 = (2 × Midpoint) − Endpoint1. Apply this separately to each coordinate. For example, if Endpoint1 is (2, 3) and the Midpoint is (5, 7), then x₂ = 2×5−2 = 8 and y₂ = 2×7−3 = 11, giving the missing endpoint (8, 11).

The endpoint formula is derived from rearranging the midpoint formula. Since M = (x₁+x₂)/2, multiplying both sides by 2 and solving for x₂ gives x₂ = 2M−x₁. The same applies to y and z coordinates independently.

In three dimensions, apply the endpoint formula to each axis separately: x₂ = 2Mₐ−x₁, y₂ = 2Mʏ−y₁, and z₂ = 2Mₑ−z₁. The principle is identical to 2D — the midpoint is the average of corresponding coordinates on every axis.

The midpoint formula averages the two endpoints: M = (P1 + P2)/2. Multiplying both sides by 2: 2M = P1 + P2. Subtracting P1 from both sides: P2 = 2M − P1. You multiply by 2 to reverse the averaging operation that produced the midpoint.

Endpoints are the two terminal points that define a line segment — they mark where the segment starts and ends. The midpoint is the single point exactly halfway between the two endpoints, equidistant from both. The midpoint divides the segment into two equal halves.

Calculate the midpoint of your two endpoints using M = ((x₁+x₂)/2, (y₁+y₂)/2). If this equals the given midpoint, your answer is correct. The calculator above shows this verification automatically. If the midpoints match, the endpoint calculation is confirmed.

Yes, the endpoint formula works with any real numbers including negatives, decimals, and fractions. For example, if Endpoint1 is (−4, 6) and Midpoint is (1, 2), then x₂ = 2×1−(−4) = 6 and y₂ = 2×2−6 = −2, giving (6, −2). Verification: midpoint of (−4,6) and (6,−2) = (1, 2) ✓.

If the midpoint equals the known endpoint (for example, both are (3, 5)), then the missing endpoint must also be (3, 5). This means both endpoints coincide, making the "line segment" a single point (a degenerate segment of length zero). The formula still works: x₂ = 2×3−3 = 3, y₂ = 2×5−5 = 5.

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