Reflections
Flip a figure across a line.
Key idea
Flip a figure across a line.
In depth
A reflection flips a shape across a mirror line, mapping each point to the point the same distance on the other side. It reverses orientation but keeps lengths and angles.
Worked example
Reflecting (3, 2) in the y-axis gives (−3, 2); in the x-axis, (3, −2); in y = x, (2, 3).
Real-world uses
- Creating symmetrical logos
- Mirror images in optics and car wing mirrors
Common mistake
Measuring distance to the mirror line incorrectly (it must be perpendicular).
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Reflections?
Flip a figure across a line. It is a topic at the intermediate level in Geometry.
Where is Reflections used in real life?
Real-world examples: Creating symmetrical logos; Mirror images in optics and car wing mirrors.
What should I learn before Reflections?
Make sure you are comfortable with Translations, the previous topic in Geometry.
What is a common mistake with Reflections?
Measuring distance to the mirror line incorrectly (it must be perpendicular).
How can I practise Reflections?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Reflections?
Move on to Rotations next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.