Activation—Unit 5 Day 1 August 5 th, 2013 Draw a coordinate plane and answer the following: 1. What are the new coordinates if (2,2) moves right 3 units? 2. What if (2,2) moves down 6 units? 3. How far and in what directions does the shape on the left have to move to make the shape on the right?

Unit 5 - Introducing Transformations August 5th, 2013

Unit 5 Day 1 August 5 th I can recognize essential geometry definitions and perform and recognize translations. G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Essential Definitions Know the lingo! Practice matching the word to the right definition. Memorize the words and their definitions. (You will need them in Units 5 & 6)

What are transformations? Transformations are the mapping, or movement, of all points of a figure in a plane according to a common operation, such as translation, reflection or rotation. Examples: Which transformations are these examples of?

Introducing Reflections: A reflection is a transformation of a figure that creates a mirror image, “flips,” over a line. Examples:

Introducing Reflections: A reflection is a transformation of a figure that creates a mirror image, “flips,” over a line. Examples:

Introducing Reflections: A reflection is a transformation of a figure that creates a mirror image, “flips,” over a line. Examples:

Introducing Reflections: A reflection is a transformation of a figure that creates a mirror image, “flips,” over a line. Examples:

Introducing Rotations: A rotation is a transformation that turns a figure about a fixed point through a given angle and a given direction, such as 90° clockwise about the origin. Examples:

Introducing Rotations: A rotation is a transformation that turns a figure about a fixed point through a given angle and a given direction, such as 90° clockwise about the origin. Examples:

Introducing Rotations: A rotation is a transformation that turns a figure about a fixed point through a given angle and a given direction, such as 90° clockwise about the origin. Examples:

Introducing Dilations: A dilation is a similarity transformation in which a figure is enlarged or reduced using a scale factor ≠ 0, without altering the center. Examples:

Introducing Dilations: A dilation is a similarity transformation in which a figure is enlarged or reduced using a scale factor ≠ 0, without altering the center. Examples:

Introducing Dilations: A dilation is a similarity transformation in which a figure is enlarged or reduced using a scale factor ≠ 0, without altering the center. Examples:

Introducing Symmetries: Symmetry is when one shape becomes exactly like another if you flip, slide or turn it. Examples:

Introducing Symmetries: Symmetry is when one shape becomes exactly like another if you flip, slide or turn it. Examples:

Introducing Symmetries: Symmetry is when one shape becomes exactly like another if you flip, slide or turn it. Examples:

Introducing Translations: A translation is a transformation that slides each point of a figure the same distance in the same direction. Most people find translations to be the easiest transformation because the shape just "slides!"

Introducing Translations: A translation is a transformation that slides each point of a figure the same distance in the same direction. Most people find translations to be the easiest transformation because the shape just "slides!"

Introducing Translations: A translation is a transformation that slides each point of a figure the same distance in the same direction. Most people find translations to be the easiest transformation because the shape just "slides!"

Translation Examples: 1. 2.

Translation Examples: 3. 4.

Translation Algebra: Sometimes we just want to write down the translation, without showing it on a graph. Example: if we want to say that the shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write:

Translation Algebra: Sometimes we just want to write down the translation, without showing it on a graph. Example: if we want to say that the shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write: This says "all the x and y coordinates will become x+30 and y+40." (See Graph)

Translation Algebra: Sometimes we just want to write down the translation, without showing it on a graph. Example: if we want to say that the shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write: This says "all the x and y coordinates will become x+30 and y+40." (See Graph)

Translation Practice #1: Describe first using words then using algebra how each of these are translated: Light preimage Dark image

Translation Practice #1 Answer : Describe first using words then using algebra how each of these are translated: Light preimage1. Right 2 units, up 4 units 2. (x + 2, y + 4)

Translation Practice #2: Describe first using words then using algebra how each of these are translated: Preimage = ABCD Image = A'B'C'D'

Translation Practice #2 Answer: Describe first using words then using algebra how each of these are translated: Preimage = ABCD 1. Right 6 units, down 4 units 2. (x + 6, y - 4)

Homework: Transformations - Translations and Definitions

Closing: Draw a coordinate plane that spans 6 units in each direction. Then graph each number and translate the following: 1. E(2, 3) - translate 5 units left 2. F(-1, -3) - translate 3 units up 3. Draw the square A(0,0), B(2,0), C(2,2), D(0,2) - translate right 3 units and 4 units down