UNIT 5 CONGRUENCE, PROOF, AND CONSTRUCTIONS Lesson 2: Defining and Applying Rotations, Reflections, and Translations Instruction

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1 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations Prerequisite Skills This lesson requires the use of the following skills: understanding the coordinate plane visual recognition of tilt vs. flip understanding the definitions of basic transformations Introduction First we learned that transformations can be functions in the coordinate plane. Then we learned the definitions and properties of three isometric transformations: rotations, reflections, and translations. Now we are able to appl what we have learned to graph geometric figures and images created through transformations. Ke oncepts Transformations can be precisel and accuratel graphed using the definitions learned. Given a set of points and a target, we can determine the transformation(s) necessar to move the given set of points to the target. Observing the orientations of the preimage and image is the first tool in determining the transformations required. Graphs can be interpreted differentl, allowing for man transformation solution sets. While there are man different solution sets of transformations that will satisf a particular graph, we will look for the more concise possibilities. Formulas can be used to determine translations, reflections, and rotations. Translation: T h, k (, ) = ( + h, + k) Reflection: through the -ais: r -ais (, ) = (, ) through the -ais: r -ais (, ) = (, ) through the line = : r = (, ) = (, ) U- USS Secondar Mathematics I Teacher Resource..

2 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations Rotation: rotation about the origin: R (, ) = (, ) rotation about the origin: R (, ) = (, ) rotation about the origin: R (, ) = (, ) ommon Errors/Misconceptions using the incorrect transformation formula for reflections using the incorrect transformation formula for rotations translating in the positive directions along the aes when the translations are intended to be in the negative directions appling the transformations in the wrong order U- USS Secondar Mathematics I Teacher Resource..

3 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations Guided Practice.. Eample Use the definitions ou have learned to graph the translation T, ( ) for which has the points (, ), (, ), and (, ).. On graph paper, draw the - and -aes and graph with the points (, ), (, ), and (, ).. Determine the new points. T, ( )= where = T = +,+ =,, = T = +,+ =,, = T = +,+ =,, U- USS Secondar Mathematics I Teacher Resource..

4 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations. Plot the new points,, and. ' ' '. onnect the vertices to graph the translation T, of. ' ' ' U- USS Secondar Mathematics I Teacher Resource..

5 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations Eample Use the definitions ou have learned to graph the reflection of parallelogram D, or D, through the -ais given D with the points (, ), (, ), (, ), and D (, ).. Using graph paper, draw the - and -aes and graph D with (, ), (, ), (, ), and D (, ). D. Write the new points. r -ais ( D)= D where = r = r, =, =, -ais = r = r, =, =, -ais = r = r, =, =, -ais D = r D = r, =, =, -ais -ais -ais -ais -ais U- USS Secondar Mathematics I Teacher Resource..

6 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations. Plot the new points,,, and D. D ' ' ' D'. onnect the corners of the points to graph the reflection r -ais of D. D ' ' ' D' U- USS Secondar Mathematics I Teacher Resource..

7 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations Eample Using the definitions ou have learned, graph a rotation of with the points (, ), (, ), and (, ).. Using graph paper, draw the - and -aes and graph with the points (, ), (, ), and (, ).. Write the new points. R ( )= where = R = R, =, = R = R, =, = R = R, =, U- USS Secondar Mathematics I Teacher Resource..

8 UNIT ONGRUENE, PROOF, ND ONSTRUTIONS Lesson : Defining and ppling Rotations, Reflections, and Translations. Plot the new points,, and. ' ' '. onnect the vertices to graph a rotation of. ' ' ' U- USS Secondar Mathematics I Teacher Resource..

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