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Math 10F
Transformational Geometry Examples
Translations• Translations are “slides”• Described by a length and
direction• Eg. translate the
following shape 6units left, and 6 units down…
Translations• 6 units left…
Translations• 6 units left…• 6 units down
Translations• 6 units left…• 6 units down• Do the same
translation for each key point
Translations• Another example: Translate this
shape 5 units left, and 3 units up
Translations• 5 left and 3 up• One point
Translations• 5 left and 3 up• Two Points
Translations• 5 left and 3 up• 3 Points
Translations• 5 left and 3 up• All Points (Connect)
Translations• Mapping Notation• (x,y) (x+2,y- 4)
Translations• Mapping Notation• (x,y) (x+2,y- 4)• This means
“right 2”, “down 4”
Translations• Mapping Notation• (x,y) (x+2,y- 4)• This means
“right 2”, “down 4”• All 4 key points
Translations• Mapping Notation• (x,y) (x+2,y- 4)• This means
“right 2”, “down 4”• All 4 key points• Connect
Translations• Show the following translations:• (x,y) (x+2, y+6)• Up 4, left 3• [-4,-1] (ordered
pair notation)
Translations• Show the following translations:• (x,y) (x+2, y+6)• Up 4, left 3• [-4,-1] (ordered
pair notation)
Translations• Show the following translations:• (x,y) (x+2, y+6)• Up 4, left 3• [-4,-1] (ordered
pair notation)
Translations• Show the following translations:• (x,y) (x+2, y+6)• Up 4, left 3• [-4,-1] (ordered
pair notation)
Reflections
• Reflections are transformations in which a figure is reflected or flipped over a reflection line.
• Each point in the new figure is the same perpendicular distance from the reflection line as the old point, except on the other side of the line.
Reflections• Reflect the shape through the y-
axis.
Reflections• Reflect the shape through the y-
axis.• Find the
perpendiculardistances of thekey points.
Reflections• Reflect the shape through the y-
axis.• Find the
perpendiculardistances of thekey points.
• Find correspondingdistanceson the other side.
Reflections• Reflect the shape through the y-
axis.• Find the
perpendiculardistances of thekey points.
• Find correspondingdistanceson the other side.
• Connect the points
Reflections• Reflect the shape through the x-
axis.
Reflections• Reflect the shape through the x-
axis.• Find the
perpendiculardistances of thekey points.
Reflections• Reflect the shape through the x-
axis.• Find the
perpendiculardistances of thekey points.
• Find correspondingdistanceson the other side.
Reflections• Reflect the shape through the x-
axis.• Find the
perpendiculardistances of thekey points.
• Find correspondingdistanceson the other side.
• Connect the points
Reflections• Reflect the shape through the
given reflection line.
Reflections• Reflect the shape through the
given reflection line.• Find the
perpendiculardistances of thekey points.
Reflections• Reflect the shape through the
given reflection line.• Find the
perpendiculardistances of thekey points.
• Find correspondingdistanceson the other side.
Reflections• Reflect the shape through the
given reflection line.• Find the
perpendiculardistances of thekey points.
• Find correspondingdistanceson the other side.
• Connect the points
Rotations• A rotation is a transformation in
which a figure is turned or rotated about a point.
• Rotations areCW or CCW
• All rotations turnrelative to thecentre of rotation.
• All rotations in thiscourse will be in90º increments.
Rotations• Rotate the figure 90º CCW through
the origin
Rotations• Rotate the figure 90º CCW through
the origin• Pick a key point• Measure a horizontal
distance and a vertical distanceto the turn centre
Rotations• Rotate the figure 90º CCW through the
origin• Pick a key point• Measure a horizontal
distance and a vertical distanceto the turn centre
• The horizontaldistance becomesyour new vertical,and your old verticalbecomes your new horizontal.
Rotations• Rotate the figure 90º CCW through
the origin
• Do this for EACHkey point
Rotations• Rotate the figure 90º CCW through
the origin
• Do this for EACHkey point
Rotations• Rotate the figure 90º CCW through
the origin
• Connect the newpoints to showthe rotated figure
Rotations• Rotate the figure 180º CW through
the origin
Rotations• Rotate the figure 180º CW through
the origin
Rotations• Rotate the figure 90º CW through
(0,2)
Rotations• Rotate the figure 90º CW through
(0,2)
Rotations• Rotate the figure 90º CW through
(3,3)
Rotations• Rotate the figure 90º CW through
(3,3)
Dilations• Dilations are enlargements or
reductions of a figure• The dilation is
enlarged by the scale factor(a multiplier)
• In this class, alldilations will occurabout the origin.
Dilations• Dilate the following figure by a
scale factor of 3
Dilations• Dilate the following figure by a
scale factor of 3
Dilations• Dilate the following figure by a
scale factor of 1/2
Dilations• Dilate the following figure by a
scale factor of ½• Notice that for
dilations, if your scale factor is >1,you are magnifying,and if your SF <1,you are shrinking
Dilations• Dilations can be expressed using a
mapping notation• Eg. perform the
following dilationon the figure given(x,y)(2x,2y)
Dilations• Dilations can be expressed using a
mapping notation• Eg. perform the
following dilationon the figure given(x,y)(2x,2y)
Dilations• For your dilations, the distances
from the origin for all key points will be proportional betweenyour two figures
