Reflections (CIE IGCSE Maths: Core)

What is a reflection?

• A reflection is a mirror image of an object across a line of reflection/mirror line
• The reflected image  is the same shape and size as the original object but it has been "flipped" across the mirror line to a new position and orientation
• Points on the mirror line do not move, they stay where they are!

How do I reflect a shape?

• You need to be able to perform a reflection (on a coordinate grid)
• The perpendicular distance between a point on the original object and the mirror line, should be the same as the perpendicular distance between the corresponding point on the reflected image and the mirror line
  
  
• STEP 1:

  From a point on the original object measure the perpendicular distance to the mirror line

• STEP 2:

  Continuing from that point on the mirror line, and in the same direction, measure the same distance again

• STEP 3:

  Mark the corresponding point on the reflected image at the position you have reached

• STEP 4:
  Join together the reflected points and label the reflected image
  

1. Vertical lines (of the form , for some number )

• • The perpendicular distance can be found by counting the number of squares horizontally from a point on the original object until you reach the mirror line

2. Horizontal lines (of the form , for some number )

• • The perpendicular distance can be found by counting the number of squares vertically from a point on the original object until you reach the mirror line

3. Double Reflections 

• • Double reflections are where the mirror line passes through the shape being reflected
  • Part of the shape gets reflected on one side of the mirror line, the other part gets reflected on the other side

   4. Regular polygons

• • Squares and other regular polygons can look identical even after a reflection (and other transformations too) – there is no obvious sign the shape has been reflected – you may think a shape has been translated
  • The way to identify these is to look at one vertex (point) on the shape and its corresponding position
    • If it is a reflection it will be “back-to-front” on the other side

How do I describe a reflection?

• You will need to be able to identify and describe a reflection when presented with one
• You must fully describe a transformation to get full marks
• For a reflection, you must:
  • State that the transformation is a reflection
  • Give the mathematical equation of the mirror line
    • Horizontal lines are of the form 
    • Vertical lines are of the form