Reflections

Reflectionsvideo

Reflections

What is a reflection?

• A reflection flips a shape across a mirror line

  • This is called the line of reflection

• The reflected image is the same size as the original object

  • It has been flipped across the mirror line to a new position and orientation

• The following two distances will be equal for each point:

  • The perpendicular distance between the original point and the mirror line 

  • The perpendicular distance between the reflected point and the mirror line

• Any points that are on the mirror line do not move

  • These are called invariant points

How do I reflect a shape?

• STEP 1
  Draw the line of reflection

  • This will usually be a vertical line ($x=k$) or a horizontal line ($y=k$)

  • A diagonal line will either be $y=x$ or $y=-x$

• STEP 2
  From each vertex on the original object measure the perpendicular distance to the mirror line

  • You can usually do this by counting squares on the grid

  • If the line is diagonal then count the diagonals of the squares

• STEP 3

  Find the reflected point by measuring the same distance in the same direction from the point on the mirror line

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

How do I reflect a shape when the line of reflection goes through the shape?

• You follow the same steps as above

• Part of the shape gets reflected on one side of the mirror line, and the other part gets reflected on the other side

How do I describe a reflection?

• To describe a reflection, you must:

  • State that the transformation is a reflection

  • Give the mathematical equation of the mirror line

• To find the equation of the reflection line:

  • Horizontal lines are of the form $y=k$

    • $k$ is the number that the line passes through on the y-axis

  • Vertical lines are of the form $x=k$

    • $k$ is the number that the line passes through on the x-axis

  • A diagonal line with a positive gradient will be $y=x$

  • A diagonal line with a negative gradient will be $y=-x$

How do I reverse a reflection?

• If a shape has been reflected to a new position, you can perform a single transformation to return the shape to its original position

  • You can reverse the reflection

• The transformation to reverse a reflection, is the same transformation as the original

  • E.g. If a shape is reflected in the x-axis, then reflecting it again in the x-axis will return it to its original position