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GEOMETRY UNIT 1

Transformations

notes

Types of Transformations

Reflections (flips): These are like mirror images as seen across a line or a point.

Translations (slides): This moves the figure to a new location with no change to the looks of the figure.

Rotations (turns): This turns the figure clockwise or counter-clockwise but doesn’t change the figure.

Dilations (zooms): This reduces or enlarges the figure to a similar figure.

The Vocabulary of Transformation Geometry

• The original figure is called the pre-image; the new (copied) picture is called the image of the transformation.

• A rigid transformation is one in which the pre-image and the image both have the exact same size and shape.

• In short, a transformation is a copy of a geometric figure, where

the copy holds certain properties. Think of when you copy/paste a picture on your

computer.

• A rigid transformation is one in which the pre-image and the image both have the exact same size and shape.

notes

Translations - Each Point is Moved the Same Way

• The most basic transformation is the translation. The formal definition of a translation is "every point of the pre-image is moved the same distance in the same direction to form the image."

• Each translation follows a rule. In this case, the rule is "5 to the right and 3 up." You can also translate a pre-image to the left, down, or any combination of two of the four directions.

x

y

Pre-image

A (-2, 4)

B (-3, 2)

C (-1, 1)

Image

A’ (3, 4)

B’ (2, 2)

C’ (4, 1)

Translation

(x, y) (x + 5, y + 0)

A

B C

A’

B’

C’

x

y

Image

A’ (-2, -1)

B’ (-3, -3)

C’ (-1, -4)

Translation

(x, y) (x + 0, y - 5)

A

B C

A’

B’ C’

Pre-image

A (-2, 4)

B (-3, 2)

C (-1, 1)

x

y

Pre-image

A (-2, 4)

B (-3, 2)

C (-1, 1)

Image

A’ (1, 0)

B’ (0, -2)

C’ (2, -3)

Translation

(x, y) (x + 3, y - 4)

A

B C

A’

B’

C’

Which of the figures below is the pre-image? Which is the image? What is the difference? How can you recognize which is which????

notes

A (-2,-1)

D (-2,-4)

B (4,-1)

C (4,-4)

A’ (1,4) B’ (7,4)

C’ (7,1)D’ (1,1)

What is the RULE for the translation to the left?

(x,y) (x + ____ , y + ____ )? ?

What is the RULE for the translation above?notes

• You and your partner will now be given a sheet of large graph paper. You MUST work together to complete this assignment. • Write your first and last names on the back of the grid paper IN

PENCIL!!!!• Create a large coordinate plane on your graph paper with the origin (0,0)

near the center of the paper. You will end up with four quadrants and both positive and negative numbers. Write numbers on both the x-axis and y-axis. Your finished product should look similar to the graph below:

• Draw a red triangle using the coordinates A =(5,5) B=(7,5) C=(7, 10)• Translate the red triangle using the rule (x,y) (x + 3, y + 4). Draw the new

triangle in red and label the vertices A’, B’, C’.• Draw a blue quadrilateral. D=(-1,0) E=(-1,3) F=(-4,3) G=(-4,0)• Translate the blue quadrilateral using the rule (x,y) (x + 0, y - 7). Draw

your new shape and label the new points with D’, E’, F’, G’.• Draw an irregular pentagon in orange. M=(8,-7) N=(11,-9) O=(9,-11)

P=(8,-9) Q=(5,-9)• Translate the concave orange pentagon into quadrant II. Be sure to keep it

the EXACT same size and shape. Label your new points “prime” and write the rule you followed on the graph next to your shape.• Draw one more polygon shape in purple, translate it, and write your rule

next to the translation.• When you have finished this poster, raise your hands and have a teacher

check your work.