Reflections
A reflection flips a figure over a line of reflection.
About this topic
A reflection flips a figure over a line of reflection, the mirror line, so each point and its image are the same distance from the line on opposite sides. The image is congruent but reversed in orientation. Over the x-axis (x, y) → (x, −y), over the y-axis (x, y) → (−x, y), and over y = x (x, y) → (y, x).
Reflections explain mirror images, symmetry in nature and the way light bounces off surfaces.
Worked example: reflect the point (3, 5) across the x-axis to get (3, −5), across the y-axis to get (−3, 5), and across the line y = x to get (5, 3). Reflect triangle (1, 1), (4, 1), (1, 3) over the y-axis to get (−1, 1), (−4, 1), (−1, 3). The mirror line is the perpendicular bisector of each point and its image.
Mirrors, lake reflections and the symmetry of faces and leaves all show the idea, and ambulances print reversed text so it reads correctly in a rear view mirror. A common mistake is switching the wrong coordinate: reflecting over the x-axis changes only y. Another is to forget the orientation reverses, so clockwise labels become counterclockwise. To check, measure that each point and its image are equal distances from the mirror, and that the segment joining them crosses the line at a right angle.
Key ideas
- Distance to the mirror line is preserved
- Reflecting over the y-axis negates x
- Orientation reverses
Quick check
Use cases: where Reflections helps
- Homework: review the key idea behind Reflections before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Reflections without notes.
- Visual learning: play with the interactive lab to see how Reflections changes when you adjust its inputs.
- Teaching a friend: explain Reflections in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Reflections?
A reflection flips a figure over a line of reflection.
What will I learn in Reflections?
Distance to the mirror line is preserved. Reflecting over the y-axis negates x. Orientation reverses.
Is Reflections part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Reflections lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Reflections?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.