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Last updated: July 31, 2026

Endpoint Calculator

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Formula

x2 = 2*mx - x1; y2 = 2*my - y1

Where:

  • mx=mx
  • my=my
  • x1=x1
  • y1=y1
EndpointA line segment showing a known endpoint, its midpoint, and the missing endpoint found by reflecting through the midpoint.(x₁, y₁)(mₓ, m_y)(x₂, y₂)Formulax₂ = 2mₓ − x₁y₂ = 2m_y − y₁
Reflecting a known endpoint through the midpoint finds the missing endpoint of a segment.

Worked Examples

Positive coordinates

Midpoint (3,4), known endpoint (1,2).

  1. 1x2 = 2(3)-1
  2. 2y2 = 2(4)-2
Final Answer: x2=5, y2=6

Mixed signs

Midpoint (-1,2), endpoint (3,-4).

  1. 1x2 = -2-3
  2. 2y2 = 4-(-4)
Final Answer: x2=-5, y2=8

Decimal coordinates

Midpoint (2.5,-1.5), endpoint (0.5,3).

  1. 1Apply both formulas directly
Final Answer: x2=4.5, y2=-6

Introduction

Find the unknown endpoint of a segment when midpoint and one endpoint are known.

Formula and Method

Endpoint Calculator uses: x2 = 2*mx - x1; y2 = 2*my - y1

  • Enter all required inputs

  • Apply the underlying math formula(s)

  • Compute supporting terms where needed

  • Round numeric outputs for stable display

Input Fields

Provide values for: mx, my, x1, y1.

  1. 1

    mx: mx

  2. 2

    my: my

  3. 3

    x1: x1

  4. 4

    y1: y1

Output Fields

The calculator returns: x2, y2.

  1. 1

    x2: x-coordinate of the missing endpoint

  2. 2

    y2: y-coordinate of the missing endpoint

Validation Rules

Input validation is applied before calculation to prevent invalid math states.

  • All coordinates must be finite numbers.

  • Uses midpoint rearrangement exactly (no approximation).

  • Supports negative and decimal coordinates.

  • Outputs are rounded to 6 decimals.

How to Use This Calculator

Fill in the inputs, run the calculator, and review primary output first.

  • Enter the required values

  • Click calculate

  • Check the primary output

  • Use example scenarios for verification

Practical Uses

This calculator supports learning, quick checks, and day-to-day technical problem solving.

  • Homework and exam preparation

  • Engineering and science sanity checks

  • Classroom demonstrations

  • Fast recalculation with different inputs

FAQs

What does the Endpoint Calculator compute?

Find the unknown endpoint of a segment when midpoint and one endpoint are known.

Which inputs are required?

Required inputs: mx, my, x1, y1.

How should I format numbers?

Use finite numeric values; decimals and negative numbers are allowed unless restricted by validation rules.

How are results rounded?

Numeric outputs are rounded to about 6 decimal places for readability.

Why might I see an error?

All coordinates must be finite numbers.

Can I use this for learning and verification?

Yes. Use the examples and formula section to verify manual calculations quickly.