Key Terms
- Mirror line: The line of symmetry about which the reflection occurs
- Perpendicular distance: The 90° distance from a point to the mirror line
- Image: The reflected shape; same size and shape as object
Must-Know Facts
- Reflect in x-axis: (x, y) → (x, −y)
- Reflect in y-axis: (x, y) → (−x, y)
- Reflect in y = x: (x, y) → (y, x)
- Reflect in y = −x: (x, y) → (−y, −x)
- x = a is a VERTICAL line; y = b is a HORIZONTAL line
- Each point moves perpendicular to the mirror line, same distance on other side
Key Methods
- Find perpendicular distance from point to mirror line
- Count squares to mirror line, count same squares the other side
- Always state: "Reflection in the line y = ..."
- Use tracing paper in exams for accuracy
Key Formulas
- Reflection in y = 0 (x-axis): (x, y) → (x, −y)
- Reflection in x = 0 (y-axis): (x, y) → (−x, y)
- Reflection in y = x: (x, y) → (y, x)
- Reflection in y = −x: (x, y) → (−y, −x)
Common Mistakes
- Wrong mirror line: Always state the full equation of the mirror line (e.g. x = 2, not just "2")
- Measuring distance wrong: Count perpendicular squares to the mirror line — not along a diagonal
- Shape changes size: Reflections preserve size and shape — if the image is different size, something is wrong
- y = x vs y = −x: These are very different mirror lines — check the direction of the diagonal
This topic summary covers Knowledge Organiser: Reflections within Transformations: Reflections for GCSE Mathematics. Revise Transformations: Reflections in Geometry & Measures for GCSE Mathematics with 13 exam-style questions and 5 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Transformations: Reflections
A point P has coordinates (3, 5). It is reflected in the x-axis. What are the coordinates of its image P'?
Fully describe the single transformation that maps shape A onto shape B. Shape A has vertices at (1, 1), (3, 1), (3, 4) and shape B has vertices at (−1, 1), (−3, 1), (−3, 4).