Position & direction
Reflecting 2D Shapes
A reflection flips a shape over a mirror line. Using a grid of squares, you can reflect each vertex the same distance on the other side of the line and join them up to draw the reflection accurately.
The mirror line rule
1. Every point and its reflection are the same distance from the mirror line. 2. They sit on opposite sides of the line. 3. A point that is on the mirror line stays exactly where it is.
Reflecting a shape on a grid
1. Count the squares from each vertex to the mirror line. 2. Mark each reflected vertex the same number of squares on the other side. 3. Join the reflected vertices to make the whole reflected shape.
Size, area and combined shapes
1. A reflection is exactly the same size and area as the original. 2. It has the same number of vertices. 3. When a shape is reflected over a mirror line along one of its edges, the shape and its reflection join to make a new shape.
Worked examples
Reflecting the vertices of a shape
- Vertex A is 2 squares from the mirror line, so its reflection is 2 squares on the other side.
- Vertex B is also 2 squares away, so its reflection is 2 squares on the other side.
- Vertex C is 3 squares away, so its reflection is 3 squares on the other side.
- Join the reflected vertices to complete the shape.
Answer: Each vertex reflects to the same distance on the opposite side of the mirror line.
Combining a shape with its reflection
- Reflect a parallelogram over a mirror line that lies along one of its edges.
- The original and the reflection meet along that edge.
- Look at the new shape they make together.
Answer: The parallelogram and its reflection make a hexagon.
The lines between vertices
- Join each original vertex to its reflected vertex with a straight line.
- Notice how each line meets the mirror line.
- The mirror line cuts each of these lines in half.
Answer: The lines cross the mirror line at right angles (they are perpendicular to it).
Where you see this in real life
- Designing symmetrical patterns for displays and fabrics.
- Checking a reflection by placing a real mirror along the mirror line.
- Creating a matching left and right side in a picture or design.
Key words
- Reflection
- A flipped copy of a shape on the other side of a mirror line.
- Mirror line
- The line a shape is reflected over.
- Vertex
- A corner of a shape where two sides meet.