transformation, object, image, translation, rotation,
reflection, line of reflection, centre of rotation, coordinates, orientation,
congruent, corresponding, equidistant, clockwise, counterclockwise
Learning Outcomes:
The student will:
Transformation
Example
original = D ABC
image = D A'B'C'
Mapping Notation
original = D ABC
image = D A'B'C'
Translation (Slide)
The object and image have the same orientation.
Corresponding sides of the object and image are parallel -->>-- .
The object and image are congruent (corresponding
angles and sides are congruent).
mapping: (x,
y) --> (x+3 ,
y +2 )
ordered
pair: [3 , 2 ]
means 3 right and 2 up
----------------------------------
Additional Mapping
Example
(x, y) --> (x -4 , y -5 )
ordered pair: [-4 , -5 ]
means
left 4 down 5 as shown by the slide arrow:
(x,
y) --> (x +3 , y +2 )
D ABC is moved 3 units right and 2 units up as shown by the
slide arrow to the left.
D ABC is located at:
A (7,4), B (5,2), C (3,
4)
Image D A'B'C' is
A' (7 +3 ,4 +2 )
B' (5 +3 ,2+2 )
C' (3 +3 ,4+2 )
or
A' (10,6), B' (8,4), C' (6, 6)
Reflection
through the x -axis (Flip)
The object and image are equidistant
from a line of reflection. Segments joining corresponding
sides of an object and image are perpendicular
to the reflection line. The object and image are congruent (corresponding
angles and sides are congruent).
mapping: (x,
y) --> (x, -y )
(x,
y) --> (x, -y )
D ABC is being flipped across the x -axis ( y = 0).
D ABC
is located at:
A (4,6), B (4,2), C (2,2)
Image D A'B'C' is
A' (4, -6 ), B' (4, -2 ), C' (2, -2 )
Reflection
through the y -axis (Flip)
The object and image are equidistant
from a line of reflection. Segments joining corresponding
sides of an object and image are perpendicular
to the reflection line. The object and
image are congruent (corresponding angles and sides
are congruent).
mapping: (x,
y) --> (-x ,
y)
( x , y) --> ( -x , y)
D ABC is being flipped across the y -axis ( x = 0).
D ABC is located at:
A (4,6), B (4,2), C (2,2)
Image D A'B'C' is
A' ( -4 ,6), B' ( -4 ,2), C' ( -2 ,2)
Reflection
through y = x (Flip)
The object and image are equidistant
from a line of reflection. Segments joining corresponding
sides of an object and image are perpendicular
to the reflection line. The object and
image are congruent (corresponding angles and sides
are congruent).
mapping: (x , y ) --> ( y ,
x )
( x , y ) --> ( y ,
x )
D ABC is being flipped across the line y = x .
D ABC is located at:
A (4,6), B (4,2), C (2,2)
Image D A'B'C' is
A' ( 6 , 4 ), B' ( 2 , 4 ), C' ( 2 , 2 )
Reflection
through y = - x (Flip)
The object and image are equidistant
from a line of reflection. Segments joining corresponding
sides of an object and image are perpendicular
to the reflection line. The object and
image are congruent (corresponding angles and sides
are congruent).
mapping: (x , y ) --> ( -y ,
-x )
( x , y ) --> ( -y ,
-x )
D ABC is being flipped across the line y = -x .
D ABC is located at:
A (4,6), B (4,2), C (2,2)
Image D A'B'C' is
A' ( -6 , -4 ), B' ( -2 , -4 ), C' ( -2 , -2 )
Reflection
through x = 1 (Flip)
The object and image are equidistant
from a line of reflection. Segments joining corresponding
sides of an object and image are perpendicular
to the reflection line. The object and
image are congruent (corresponding angles and sides
are congruent).
mapping: (x , y ) --> ( 2-x , y )
( x , y ) --> ( 2-x , y )
D ABC is being flipped across the line x =
1.
D ABC is located at:
A (4,6), B (4,2), C (2,2)
Image D A'B'C' is
A' ( -2 , 6 ), B' ( -2 , 2 ), C' ( 0 , 2 )
Rotation
about the origin
The object and image are equidistant
from a given point. The object and image are congruent (corresponding
angles and sides are congruent).
mapping
( x , y ) --> ( -x , -y )
turn center = origin
( x , y ) --> ( -x , -y )
D ABC is rotated 1/2 turn around the origin (clockwise or
counterclockwse.
D ABC is
located at:
A (-3,-4), B (-2,-1), C (-5,-5)
Image D A'B'C' is:
A' ( 3 , 4 ), B' ( 2 , 1 ), C' ( 5 , 5 )
Rotation
about the origin
The object and image are equidistant
from a given point (turn centre). The object and image are congruent (corresponding
angles and sides are congruent).
mapping: (x , y ) --> ( y , -x )
turn center = origin
( x , y ) --> ( y , -x )
D ABC is rotated 1/4 turn around the origin.
D ABC is located at:
A (-3,-4), B (-2,-1), C (-5,-5)
Image D A'B'C' is:
A' ( -4 , 3 ), B' ( -1 , 2 ), C' ( -5 , 5 )
Rotation
about the origin
The object and image are equidistant
from a given point. The object and image are congruent (corresponding
angles and sides are congruent).
mapping: (x , y ) --> (- y , x )
turn center = origin
( x , y ) --> ( -y , x )
A (-3,-4), B (-2,-1), C (-5,-5)
D ABC is rotated 1/4 turn
around the origin.
Image D A'B'C' is:
A' ( 4 , -3 ), B' ( 1 , -2 ), C' ( 5 , -5 )
Dilatation
about the origin (Enlargement or Reduction)
The object and image are similar (~ )
when the dilatation factor ¹ 1. (corresponding angles are congruent ).
The object and image are congruent when the dilatation
factor = 1. (corresponding angles and sides are
congruent ).
mapping: (x,
y) --> (3 x, 3 y)
dilatation centre = origin
(x,
y) --> ( 3 x, 3 y)
D ABC ~ D A'B'C'
D ABC is being enlarged by a factor of 3 relative to the origin.
A (2,3), B (2,1), C (1,1)
Image D A'B'C' is
A' ( 6 , 9 ), B' ( 6 , 3 ), C' ( 3 , 3 )
Modified Source: The Learning
Equation 9 "Identifying Transformations"
Tesselations
A tessellation is a tiling pattern that can be made by
slides, flips or turns.
Click and drag the four tiles below until the pieces are
joined together to make a square.
return
to menu
half
turn clockwise (cw) or 
half turn counterclockwise (ccw)
quarter turn clockwise (cw) or 
three
quarter turn counterclockwise (ccw)
quarter turn counterclockwise (ccw) or 
three quarter turn clockwise (cw)
