EDEXCEL GCSE FOUNDATION MATHS - What are Reflections

Edexcel GCSE Foundation Maths: Reflections

What are Reflections?

A reflection is a transformation that flips a shape over a line called the line of reflection. The reflected shape is the same size and shape as the original, but it's facing the opposite direction.

How to Reflect a Shape

1. Identify the line of reflection. This can be a vertical, horizontal, or diagonal line.
2. Measure the distance from each point of the original shape to the line of reflection.
3. Mark the corresponding points on the other side of the line of reflection, at the same distance. These points will be the vertices of the reflected shape.
4. Join the points to form the reflected shape.

Example

Let's reflect triangle ABC over the y-axis:

           B 
          / \
         /   \
        /     \
       A-------C

      y-axis 

1. Identify the line of reflection: The y-axis is the line of reflection.
2. Measure the distance:
   • Point A is 2 units to the left of the y-axis.
   • Point B is 3 units to the right of the y-axis.
   • Point C is 1 unit to the right of the y-axis.
3. Mark corresponding points:
   • Mark a point 2 units to the right of the y-axis, corresponding to point A.
   • Mark a point 3 units to the left of the y-axis, corresponding to point B.
   • Mark a point 1 unit to the left of the y-axis, corresponding to point C.
4. Join the points: Connect the three points to form the reflected triangle.

          B'  
          / \
         /   \
        /     \
       A'------C' 

       y-axis 
       A-------C

The reflected triangle is labelled A'B'C'. Notice that the shape and size are the same as the original triangle, but it's facing the opposite direction.

Key Properties of Reflections

• Congruence: The original shape and the reflected shape are congruent, meaning they have the same size and shape.
• Distance: The distance between a point on the original shape and the line of reflection is equal to the distance between the corresponding point on the reflected shape and the line of reflection.
• Orientation: The reflection reverses the orientation of the shape.

Practice

Try reflecting different shapes over various lines of reflection. You can use graph paper or online tools to help you visualize the process.