Transformations
Reflections
A reflection is a mirror image of a shape. Every point moves to the same distance on the other side of the mirror line, so the shape stays the same size ā it is just flipped.
Three kinds of mirror line
You can reflect a shape in a mirror line that is: ā¢ horizontal (going from side to side), ā¢ vertical (going up and down), or ā¢ diagonal (going at a slant). The mirror line acts like a line of symmetry between the shape and its reflection.
The equal-distance rule
Every point and its reflection are the same distance from the mirror line, on opposite sides. So the mirror line lies exactly halfway between a point and its reflected point. One good way to reflect a vertex: draw an arrow from it to the mirror line, then draw an arrow the same length on the other side.
What stays the same
A reflection is a mirror image, so the reflected shape is exactly the same size and shape as the original ā only flipped. Tracing paper or a mirror can help you check your work.
Worked examples
Reflecting in a vertical mirror line
- A vertex is 3 squares to the left of a vertical mirror line.
- Measure that distance to the line.
- Mark the same distance on the other side.
Answer: The reflected vertex is 3 squares to the right of the mirror line.
Reflecting in a horizontal mirror line
- A point is 3 squares above a horizontal mirror line.
- How far across it is stays the same.
- Mark the reflection the same distance below the line.
Answer: The reflection is 3 squares below the mirror line.
Reflecting in a diagonal mirror line
- Take one vertex of the shape at a time.
- Draw an arrow from the vertex to the diagonal mirror line, then an equal arrow the other side.
- Join the reflected vertices with straight lines.
Answer: The completed shape is the mirror image across the diagonal line.
The size does not change
- Compare the original shape with its reflection.
- Every length is the same; the shape is only flipped.
Answer: A reflected shape is exactly the same size and shape as the original.
Where you see this in real life
- Seeing your reflection in a mirror or in still water.
- Artists adding reflections in water or shiny objects to their paintings.
- Making a symmetrical pattern by reflecting a shape in a mirror line.
Key words
- Reflection
- A mirror image of a shape across a mirror line.
- Mirror line
- The line a shape is reflected in; it acts like a line of symmetry.
- Horizontal
- Going from side to side, like the horizon.
- Vertical
- Going straight up and down.
- Diagonal
- Going at a slant, between horizontal and vertical.