vectors and transformations

• 3 details for describing rotations

  • angle of orientation
  • direction
  • centre
• hack for drawing reflections

  use tracing paper and outline the shape and reflection line then flip it over.
• hack for describing reflections centre

  Join up both shapes' points and they should meet at a coordinate.}
• steps for enlargements

  • count squares from centre to a corner
  • scale it and count squares and plot points
  • repeat for each corner of shape
  • (for negative scale factors, go opposite way of vector like up-->down)
• How do you find the magnitude of a vector?

  Pythagoras' therom
• How do you prove parallel vectors?

  1. write vector expressions for both lines
  2. check to see if they are multiples of each other
  3. conclusion; both lines are parallel as vector AB and CD is a multiple of E. AB is E times the length of CD.
• How do you prove straight line vectors?

  1. make two vector expressions
  2. show that they are parallel as multiples of each other
  3. state that they share a common point
• 5 transformations

  • vertical shift
  • horizontal shift
  • reflection
  • compression / stretch in y axis
  • compression / stretch in x axis
• Description and equation for vertical shift

  • y= f(x) +/- c
  • moves graph up / down
  • +c is up
  • -c is down
• Description and equation for horizontal shift

  • y= f(x + 1)
  • x+1 is left
  • x-1 is right
• Description and equation for reflection in y axis

  • y= f( -x )
  • graph is reflected in the y axis
• Description and equation for reflection in x axis

  • y= -f (x)
  • graph is reflected in the x axis
• Description and equation for compression/stretch in y axis

  • y = cf (x)
  • y is x larger
  • greater than 1 is stretch
  • less than 1 is compress
• Description and equation for compression/stretch in x axis

  • y= f (cx)
  • y is x larger
  • greater than 1 is compress
  • less than 1 is stretch
• Tip for functions in transformations on graph

  • Changing whole function does what you expect it to
  • Changing the x value does the opposite of what you expect it to