Transformation

original = ΔABC

image = ΔA'B'C'

Mapping Notation

original = ΔABC

image = ΔA'B'C'

• 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)

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)

A'(10,6), B'(8,4), C'(6, 6)

• 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 x-axis (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)

• 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 y-axis (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)

• 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)

• 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)

• 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)

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)

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)

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)

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)

• 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)