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Reflection
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Geometry Hub / Transformations / Reflection
07.02 • Transformations

Reflection

Use a mirror line on the plane to study how a figure flips to the opposite side while matching perpendicular distance point by point.

Interactive diagram Live labels and measurements Worked examples PNG graph downloads
Reflection
Interactive diagram

Reflection Diagram

Move the figure or the mirror line and compare each point with its image across the line of reflection.

Use the movable diagram to see what defines reflection, how the labels relate to the figure, and what stays true as the board changes.

Definition: A reflection flips a figure across a line.
Detailed definition

Understanding Reflection

A reflection flips a figure across a line, called the line of reflection. Each point of the image appears on the opposite side of that line at the same perpendicular distance as the original point.

Reflection preserves lengths and angle measures, so the image is congruent to the original. What changes is orientation: the figure becomes a mirror image rather than a turned copy.

This page keeps the line of reflection and the paired points on screen together so the flip can be justified by geometry, not just by appearance.

Key facts

Important ideas to remember

  • A reflection flips a figure across a line.
  • The line of reflection is the perpendicular bisector of the segment joining any point to its reflected image.
  • Reflection is a rigid motion, so side lengths and angle measures are preserved.
  • Orientation reverses under reflection, which is why letters and ordered shapes can look mirrored.
Where it is used

Where reflection shows up

  • Use reflection when finding images across the x-axis, y-axis, y = x, or another mirror line.
  • Use it in symmetry problems where a figure matches itself across a line.
  • Use it in coordinate proofs that rely on equal distance from a line or on perpendicular bisector structure.
Common mistakes

What to watch out for

  • Do not guess the reflected point by eye without checking equal perpendicular distance from the mirror line.
  • Do not confuse reflection with rotation just because the image looks repositioned.
  • Do not forget that the line of reflection sits midway between corresponding points, not on one side of them.
Worked examples

Reflection examples

Use these worked examples to see the idea in a clean diagram first, then in the kind of reasoning students usually need for classwork, homework, or test practice.

Example 1

Example 1: Identifying reflection from the mapped figure

Use the visible change between the original and image to name the transformation before writing a coordinate rule.

  • Find the original figure first.
  • Compare its position, orientation, and size with the image.
  • Use that comparison to name the motion.

Result: The transformation is read from the geometry of the mapping itself.

Example 2

Example 2: Writing the coordinate story of reflection

Move from the picture to the language of vectors, centers, reflections, or scale factors only after the motion is clear.

  • Read how key points move.
  • Describe the motion in words.
  • Translate that motion into the coordinate description that fits the page.

Result: The symbolic rule makes sense because it grows out of the visible change on the graph.

For

Why this page helps

This page helps because reflection depends on one precise geometric test: corresponding points must be the same perpendicular distance from the line of reflection. Once students see that condition, mirror-image problems become far easier to read.

Do

What you can do here

  • Drag the line of reflection and verify the equal-distance mirror rule visually.
  • Compare corresponding points before and after the flip to see why the image is congruent.
  • Keep a clean reflection diagram that shows the mirror line doing the geometric work.
Learning outcome

What this page helps you do

These takeaways are meant to help you recognize the idea faster, read diagrams more accurately, and use the topic with more confidence in real problems.

1

Reflection

Read reflection as a mirror rule instead of a vague left-right reversal.

2

Reflection

Use perpendicular-distance reasoning more confidently in coordinate reflection problems.

3

Reflection

Separate reflected images from rotated or translated images with less hesitation.

07

Back to Transformations

Return to the category page to open another concept in transformations.

ST

Geometry Construction Studio

Use a dedicated geometry drawing board for points, segments, rays, lines, angles, circles, triangles, rectangles, pencil sketches, and virtual measuring tools.

07.01

Previous: Translation

A translation slides a figure without turning or resizing it.

07.03

Next: Rotation

A rotation turns a figure around a fixed point.