IGCSE Maths / Transformation and similarity
Equations of common mirror lines
Edexcel International GCSE Maths (4MA1), chapter 14: Transformation and similarity, specification point 5.2d. Free lesson.
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A reflection is described by the equation of its mirror line. Recognising the common mirror lines helps you name the transformation accurately and reflect points correctly.
What a mirror line tells you
A mirror line is the line a shape flips over. Each point and its image lie on opposite sides of the line, the same distance away. This distance is measured at right angles to the mirror, and points already on the line stay still. To describe a reflection, give the mirror line’s equation, not just a drawing. For example, write reflection in the line x = 3.
How to reflect a shape in x = 3
The line x = 3 is upright, so every point on it has x-coordinate 3. Each vertex moves straight across to the mirror and the same distance beyond it. The x-coordinate changes, while the y-coordinate stays the same. Triangle ABC has vertices (4, 1), (7, 1) and (4, 3). A is 1 square from the mirror, so its image is 1 square on the other side. B is 4 squares from the mirror, so its image is 4 squares on the other side.
How to recognise the common mirror lines
An upright line fixes the x-coordinate, while a flat line fixes the y-coordinate, or height. The diagonal y = x has matching coordinates. The other diagonal, y = −x, has opposite coordinates. x = 3 is upright. Points on it include (3, 0) and (3, 5). A reflection maps (x, y) to (6 − x, y). y = −1 is flat. Points on it include (0, −1) and (4, −1). A reflection maps (x, y) to (x, −2 − y). y = x rises to the right. Points on it include (2, 2) and (−3, −3). A reflection swaps the coordinates: (x, y) maps to (y, x). The axis versions are x = 0, the y-axis, and y = 0, the…
How to name a line from its direction
Choose the coordinate that stays the same along the line. An upright line has a constant x-coordinate, so its equation begins x =. A flat line has a constant y-coordinate, so its equation begins y =. The upright line through 3 on the x-axis is x = 3, not y = 3. Its height changes as you move along it, but x stays 3. The flat line through 3 on the y-axis is y = 3.
How to find a mirror line from two points
Compare the coordinates of the two points. If their y-coordinates match, they are at the same height and lie on a flat line. If their x-coordinates match, they lie on an upright line. The points (0, 4) and (5, 4) have the same y-coordinate, so their line is flat and has equation y = 4.
More lessons in Transformation and similarity
- Lines of symmetry and rotational symmetry
- Reflecting a shape in a line
- Reflecting in y = x and y = -x
- Finding the mirror line from object and image
- What defines a rotation
- Rotating a shape about a point
- Positive and negative rotation angles
- Rotating about a point not on the shape
- What defines a translation
- Translating a shape
- Column vectors in translations
- Congruence under transformations
- Describing a single transformation fully
- Combining two transformations
- What defines an enlargement
- Similarity under enlargement
- Enlarging from a given centre
- Fractional scale factor enlargements
- Finding the centre of enlargement
- Conditions for congruent triangles
- Proving triangles are congruent
- Similar shapes: corresponding lengths
- Area scale factor
- Volume scale factor
- Similar solids, mass and capacity
- Similar shapes problem solving