Math

Free Coordinate Reflection & Rotation Calculator

Reflect or rotate a 2D point.

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Inputs

Result

Transformed point

(4.0000, -3.0000)

Original point(4.000, 3.000)

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Short answer

Reflect or rotate a 2D point.

What is the Coordinate Reflection & Rotation Calculator?

Reflect or rotate a 2D point.

How does the Coordinate Reflection & Rotation Calculator work?

Enter the inputs above and read the result.

Formula

Rotation: (x cosθ − y sinθ, x sinθ + y cosθ)

Variables

  • θRotation angle

Explanation

Reflections flip sign of one or both coordinates; rotation applies the standard 2D rotation matrix.

Examples

Applications

    Advantages

      Limitations

        Common mistakes

          Tips

            Related concepts

            The Coordinate Reflection & Rotation Calculator sits inside the Math Calculators hub, in the geometry & shapes cluster. Length, area, volume and angle in two and three dimensions. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.

            areaperimetervolumesurface areaanglecoordinate plane

            Practical use cases and industry applications

            Understanding Coordinate Reflection & Rotation

            Reflect or rotate a 2D point. Within math calculators, coordinate reflection & rotation belongs to the geometry & shapes cluster, where it shares terminology and assumptions with closely related tools.

            Learning how coordinate reflection & rotation is calculated

            Reflections flip sign of one or both coordinates; rotation applies the standard 2D rotation matrix. Working through the variables one at a time — θ — makes the result reproducible by hand and easier to sanity-check.

            Using coordinate reflection & rotation to make a decision

            Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.

            How coordinate reflection & rotation compares with related measures

            area, perimeter, volume, surface area all describe adjacent aspects of geometry & shapes. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.

            Frequently asked questions

            Related calculators

            More geometry & shapes tools

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