TransformationsIncluding Translations, Rotations and

Reflections

8G CCGPS Unit 1

What are Transformations?

In mathematics, a transformation changes the position or orientation of a figure. The resulting figure is the image of the original.

Images resulting from the transformations described in the next slides are congruent to the original figures.

Vocabulary

Translation Rotation Reflection Image Pre-Image Congruent Similar

Angle of Rotation Reflection Line Prime Reflectional

symmetry Center of

Rotation

Things to know

A’ is read “A prime” and is used to represent the point on the image that corresponds to point A of the original figure

The point that a figure rotates around may be on the figure or away from the figure.

Translations

TranslationThe figure slides along a straight line without turning.

Working With Translations

1. Plot polygon BAKE on a coordinate plane using vertices B(1,4), A(1,6), K(4,6), and E(4,4).

2. Label the coordinates and connect the vertices.

3. Color in the polygon.4. Translate BAKE 2 units right and 3 units

down. Label the image B’A’K’E’ (Prime).5. Compare the size, location, and coordinates

of the pre-image (original) and the image.6. What happened mathematically to the

coordinates (x,y) of the vertices after BAKE was translated?

B(1,4), A(1,6), K(4,6), and E(4,4)

B’(3,1), A’(3,3), K’(6,3),’and E’(6,1)

Rule: (x+2, y-3) .

Translate BAKE 2 units right and 3 units down. Label the image B’A’K’E’ (Prime).

• Compare the size, location, and coordinates of the pre-image (original) and the image.

• What happened mathematically to the coordinates (x,y) of the vertices after RAKE was translated?

Working With Translations

1. Plot polygon RAKE on a coordinate plane using vertices R(3,3), A(3,6), K(6,6), and E(6,3).

2. Label the coordinates and connect the vertices.

3. Color in the polygon.4. Translate RAKE 8 units left and 7 units down

and. Label the image R’A’K’E’ (Prime).5. Compare the size, location, and coordinates

of the pre-image (original) and the image.6. What happened mathematically to the

coordinates (x,y) of the vertices after RAKE was translated?

R(3,3), A(3,6), K(6,6), and E(6,3)

R’(3,3), A’(3,6), K’(6,6), and E’(6,3)

Rule: (x-8, y-7)

Translate RAKE 8 units left and 7 units down. Label the image R’A’K’E’ (Prime).

• Compare the size, location, and coordinates of the pre-image (original) and the image.

• What happened mathematically to the coordinates (x,y) of the vertices after RAKE was translated?

Reflections

ReflectionThe figure flips across a line of reflection, creating a mirror image.

Working With Reflections

1. Plot polygon PAW on a coordinate plane using vertices P(1,1), A(1,3), and W(3,1).

2. Label coordinates and connect the vertices.3. Color in the polygon.4. Reflect PAW over the x-axis.5. Label coordinates of P’A’W’ and color in the

polygon.6. How did the coordinates change on the image

C’A’K’E’?

P(1,1), A(1,3), and W(3,1)

1. Reflect PAW over the x-axis.

2. Label coordinates of P’A’W’ and color in the polygon.

How did the coordinates change on both images’?

Working With Reflections

1. Plot polygon PAW on a coordinate plane using vertices P(1,1), A(1,3), and W(3,1).

2. Label coordinates and connect the vertices.3. Color in the polygon.4. Reflect PAW over the y-axis.5. Label coordinates of P’A’W’ and color in the

polygon.6. How did the coordinates change on the image

P’A’W’?

P(1,1), A(1,3), and W(3,1)

3. Reflect PAW over the y-axis.

4. Label coordinates of P’A’W’ and color in the polygon.

How did the coordinates change on both images’?

Reflection RuleTo reflect along the x-axis:• x stays the same• y is its opposite• Example: (3,-2) = (3,2)

Pre-image WOLF W(3,3) O(3,6) L(8,6) F(8,3)

Image W’O’L’F’ W’(3,-3) O’(3,-6) L’(8,-6) F’(8,-3)

Reflection RuleTo reflect along the y-axis: y stays the same x is its opposite Example: (3,-2) = (-3,-2)

Pre-image WOLF W(3,3) O(3,6) L(8,6) F(8,3)

Image W’O’L’F’ W’(-3,3) O’(-3,6) L’(-8,6) F’(-8,3)

Transformations

The mapping, or movement, of all the points of a figure in a plane according to a common operation.

A change in position occurs in translations, reflections and rotations.

Translation (slide)

A transformation that “slides” each point of a figure the same distance in the same direction.

A translation will be a congruent figure.

Example:

Reflection (flip)

A transformation that “flips” a figure over a line of reflection.

A mirror image is created. A reflection will be a congruent

figure.

Example:

Rotation (turn)

A transformation that turns a figure about a fixed point through a given angle and a given direction.

A rotation will be a congruent figure.

Example: