Reflections (Edexcel GCSE Maths)

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. Diagonal lines (of the form , see straight line graphs)

• • Reflecting in diagonal lines can be much tricker
  • The perpendicular distance can be measured directly using a ruler
  • You can also count the number of squares horizontally and vertically until you reach the mirror line, e.g. 2 to the right, 3 down, then from the same point on the mirror line, count the number of squares vertically that was the previous horizontal distance and count the number of squares horizontally that was the previous vertical distance, e.g. 3 to the right, 2 down

4. 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

   5. 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 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

Which points are invariant with a reflection?

• Invariant points are points that do not change position when a transformation has been performed
  • Invariant points don't move!
• With a reflection, any points that lie on the mirror line (line of reflection) are invariant points, as they do not move when reflected