Transformations

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Transformations

• Math 8

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Four Types

• Translation (Slide)
• Rotation (turn)
• Reflection (flip)
• Dilation (shrinking/stretching)

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Examples
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When working with transformations it is helpful
to remember the coordinate system

• Quadrant 1 (x, y)
• Quadrant 2 (-x, y)
• Quadrant 3 (-x, -y)
• Quadrant 4 (x, -y)

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Examples
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Reflections-(Flip)

• When you reflect a shape in the coordinate plane,
  you reflect it over a line. This line is called
  the line of reflection/symmetry.
• When a figure is reflected on a coordinate plane,
  every point of the figure must have a
  corresponding point on the other side.

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• Most reflections are over the x-axis
  (horizontal), the y-axis (vertical), or the line
  y x (diagonal uphill from left to right.)

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Reflections

• When you reflect a shape over the x axis, use
  the same coordinates and multiply the y
  coordinate by 1. (x, opposite y)
• When you reflect a shape over the y-axis, use the
  same coordinates and multiply the x coordinate by
  1. (opposite x, y)
• When you reflect a shape over the line yx, use
  the same coordinates and multiply both by 1.

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Examples

• 1. Reflect the triangle over the x-axis and y
  axis.

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Examples
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Examples
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Translations (Slides/Glide)

• To translate a figure in the direction describe
  by an ordered pair, add the ordered pair to the
  coordinates of each vertex of the figure.
• The new set of ordered pairs is called the image.
  It is shown by writing A. This is read the
  image of point A.

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Examples

• Find the coordinates of the vertices of each
  figure after the translation described. Use the
  graph to help you.

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Examples

• Find the coordinates of the vertices of each
  figure after the translation described.

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Rotations (Turns)

•   ¼ turn 90 degrees rotation
•   ½ turn 180 degrees rotation
• ¾ turn 270 degrees rotation
•   full turn 360 degrees rotation
• Example
• Example

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In the coordinate plane we have 4 quadrants. If
the shape is rotated around (0,0) then

• 90 degrees rotation moves 1 quadrant
• Rotating 90? clockwise. (x, y) (y,
  opposite x)
• same as 270? counterclockwise.
• Rotating 90? counterclockwise is the
• same as 270? clockwise. (x, y) (opposite
  y, x)
• 180 degrees rotation moves 2 quadrants
  
• Multiply both by 1.
• (x, y,)  (opposite x, opposite y)
• 270 degrees rotation moves 3 quadrants
• Rotating 270? counterclockwise is the same as 90?
  clockwise
• (x, y) (y, opposite x)
• 360 degrees rotation moves 4 quadrants
• (stays the same)

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Examples

• If a triangle is in Quadrant 2 and is rotated 270
  counterclockwise, what quadrant is it now in?
• If a triangle is in Quadrant 4 and is rotated 90
  clockwise, what quadrant is it now in?

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Symmetry

• Two Types
• 1. Line Symmetry (can be called reflectional
  symmetry) if you can fold a shape and have the
  edges meet
• The place where you fold is called the line of
  symmetry

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More Line Symmetry
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InkBlots
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Does the Human Face Possess Line Symmetry?
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Answer No
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Girl
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Carpets
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Examples

• Do the following shapes have line symmetry? If
  so, how many lines of symmetry do they have?
• a. b. c. d.
  e.

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Rotational Symmetry

• 2. Rotational Symmetry If you can turn the
  shape less than 360o and still have the same
  shape.
• Order of Rotational Symmetry Is the number of
  rotations that must be made to return to the
  original orientation
• Minimum Rotational Symmetry The smallest number
  of degrees a shape can be rotated and fit exactly
  on itself
• Hint Take 360o divided by the number of
  sides/points.

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Examples
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Examples

• Does the following shape have rotational
  symmetry? If yes, what is the order and MRS?
• a. b. c. d. e.