The Transformation Simulation above is summarized in the notes below.
Transformation 
Example
 original = ΔABC
 image = ΔA'B'C'

Mapping Notation
 original = ΔABC
 image = ΔA'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) > (x4, y5)
ordered pair: [4, 5]
means left 4 down 5 as
shown by the slide arrow:

(x, y) > (x+3, y+2)
ΔABC is moved 3 units right and 2 units up as shown by the slide arrow to the
left.
ΔABC is located at:
A(7,4), B(5,2), C(3, 4)
Image ΔA'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 xaxis (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)
ΔABC is being flipped across the xaxis (y = 0).
ΔABC is located
at:
A(4,6), B(4,2), C(2,2) Image ΔA'B'C' is
A'(4,6), B'(4,2), C'(2,2) 
Reflection through
the yaxis (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)
ΔABC is being flipped across the yaxis (x = 0).
ΔABC is located at:
A(4,6), B(4,2), C(2,2)
Image ΔA'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)
ΔABC is being flipped across the line y = x.
ΔABC is located at:
A(4,6), B(4,2), C(2,2)
Image ΔA'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)
ΔABC is being flipped across the line y = x.
ΔABC is located at:
A(4,6), B(4,2), C(2,2)
Image ΔA'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) > (2x, y)

(x, y) > (2x, y)
ΔABC is being flipped across the line x
= 1.
ΔABC is located at:
A(4,6), B(4,2), C(2,2)
Image ΔA'B'C' is:
A'(2,6), B'(2,2), C'(0,2) 
Rotation about
the origin half turn
clockwise (cw) or half turn counterclockwise (ccw)
 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)
ΔABC is rotated 1/2 turn around the origin (clockwise or counterclockwse.
ΔABC is located at:
A(3,4), B(2,1), C(5,5)
Image ΔA'B'C' is:
A'(3, 4), B'(2, 1), C'(5, 5) 
Rotation
about the origin quarter turn clockwise (cw) or three
quarter turn counterclockwise (ccw)
 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)
ΔABC is rotated 1/4 turn around the origin.
ΔABC is located at:
A(3,4), B(2,1), C(5,5)
Image ΔA'B'C' is:
A'(4, 3), B'(1, 2), C'(5, 5) 
Rotation
about the origin quarter turn counterclockwise (ccw) or three quarter turn clockwise (cw)
 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)
ΔABC is rotated 1/4 turn around the origin.
Image ΔA'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) > (3x, 3y)
dilatation centre = origin 
(x, y) > (3x, 3y)
ΔABC is being enlarged around the origin.
A(2,3), B(2,1), C(1,1)
Image ΔA'B'C' is:
A'(6, 9), B'(6, 3), C'(3, 3) 
Started September, 1998. Copyright © 1999,
2000, 2001, 2002, 2003, 2004
visitors since April 15,
2002 