Illustrative Math Alignment: Grade 8 Unit 1
Rigid Transformations and Congruence
Lesson 6: Describing Transformations
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Geometric Transformation--Transformations: Example 6 | Math Example--Geometric Transformation--Transformations: Example 6TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below illustrates a reflection of the shape across a red dashed line, which represents the axis of reflection. This transformation showcases how an object can be flipped over a line while maintaining its size and shape. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 7 | Math Example--Geometric Transformation--Transformations: Example 7TopicTransformations DescriptionThis example illustrates a complex combination of transformations: translation, rotation, and reflection. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below demonstrates three sequential transformations: first, a translation moves the shape, then a rotation turns it (indicated by a pushpin showing the axis of rotation), and finally, a reflection flips it across a red dashed line representing the axis of reflection. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 8 | Math Example--Geometric Transformation--Transformations: Example 8TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. Two grids labeled "Before" and "After" show an "O" shape slightly shifted between the grids. The solution diagram below illustrates a translation of the shape from one position to another, showcasing how an object can move position without changing its size or orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 9 | Math Example--Geometric Transformation--Transformations: Example 9TopicTransformations DescriptionThis example illustrates a combination of transformations: translation and rotation. Two circular "O" shapes are shown on a grid, one labeled "Before" and the other "After". The solution involves a translation (movement) and a rotation, with a pushpin indicating the axis of rotation. This demonstrates how multiple transformations can be applied sequentially to a shape. |
Definition of Transformations |
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Math Example--Geometric Transformation--Translating Triangles--Example 1 | Math Example--Geometric Transformation--Translating Triangles--Example 1TopicTransformations DescriptionA triangle on a grid is translated 4 units to the left. It shows the original triangle ABC and the translated triangle A'B'C'. Example 1: "Draw the triangle that results from the following translation: 4 units to the left." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 10 | Math Example--Geometric Transformation--Translating Triangles--Example 10TopicTransformations Description
The triangle is translated 4 units to the left and 2 units up. It displays both the initial and the translated triangles. Example 10: "Draw the triangle that results from the following translation: 4 units to the left, 2 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 11 | Math Example--Geometric Transformation--Translating Triangles--Example 11TopicTransformations DescriptionTriangle ABC is translated horizontally to the right by 4 units to form triangle A'B'C'. Example 11: The translation is described as 4 units to the right. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 12 | Math Example--Geometric Transformation--Translating Triangles--Example 12TopicTransformations DescriptionTriangle ABC is translated vertically downward by 6 units to form triangle A'B'C'. Example 12: The translation is described as 6 units down. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 13 | Math Example--Geometric Transformation--Translating Triangles--Example 13TopicTransformations DescriptionTriangle ABC is translated horizontally to the left by 5 units to form triangle A'B'C'. Example 13: The translation is described as 5 units to the left. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 14 | Math Example--Geometric Transformation--Translating Triangles--Example 14TopicTransformations DescriptionTriangle ABC is translated vertically upward by 6 units to form triangle A'B'C'. Example 14: The translation is described as 6 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 15 | Math Example--Geometric Transformation--Translating Triangles--Example 15TopicTransformations Description
Triangle ABC is translated diagonally 5 units to the right and 5 units downward to form triangle A'B'C'. Example 15: The translation is described as 5 units to the right and 5 units down. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 16 | Math Example--Geometric Transformation--Translating Triangles--Example 16TopicTransformations DescriptionTriangle ABC is translated diagonally 4 units to the right and 3 units upward to form triangle A'B'C'. Example 16: The translation is described as 4 units to the right and 3 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 17 | Math Example--Geometric Transformation--Translating Triangles--Example 17TopicTransformations DescriptionTriangle ABC is translated diagonally 4 units downward and 4 units to the right to form triangle A'B'C'. Example 17: The translation is described as 4 units down and 4 units to the right. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 18 | Math Example--Geometric Transformation--Translating Triangles--Example 18TopicTransformations Description
Triangle ABC is translated diagonally 3 units upward and 3 units to the right to form triangle A'B'C'. Example 18: The translation is described as 3 units up and 3 units to the right. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 19 | Math Example--Geometric Transformation--Translating Triangles--Example 19TopicTransformations DescriptionTriangle ABC is translated diagonally 6 units to the left and 4 units downward to form triangle A'B'C'. Example 19: The translation is described as 6 units to the left and 4 units down. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 2 | Math Example--Geometric Transformation--Translating Triangles--Example 2TopicTransformations DescriptionA triangle on a grid is translated 5 units to the right. The diagram shows the original triangle ABC and the new position, A'B'C'.. Example 2: "Draw the triangle that results from the following translation: 5 units to the right." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 20 | Math Example--Geometric Transformation--Translating Triangles--Example 20TopicTransformations DescriptionTriangle ABC is translated diagonally 2 units to the left and 5 units upward to form triangle A'B'C'. Example 20: The translation is described as 2 units to the left and 5 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 21 | Math Example--Geometric Transformation--Translating Triangles--Example 21TopicTransformations |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 22 | Math Example--Geometric Transformation--Translating Triangles--Example 22TopicTransformations |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 3 | Math Example--Geometric Transformation--Translating Triangles--Example 3TopicTransformations DescriptionA triangle on a grid is translated 4 units up. The figure displays both the original and translated triangles ABC and A'B'C'.. Example 3: "Draw the triangle that results from the following translation: 4 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 4 | Math Example--Geometric Transformation--Translating Triangles--Example 4TopicTransformations DescriptionA triangle on a grid is translated 5 units down. It shows the original triangle and its new position after translation, labeled A'B'C'. Example 4: "Draw the triangle that results from the following translation: 5 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 5 | Math Example--Geometric Transformation--Translating Triangles--Example 5TopicTransformations DescriptionA triangle is translated 4 units to the left and 2 units down. Both the original and the new triangles, ABC and A'B'C', are illustrated. Example 5: "Draw the triangle that results from the following translation: 4 units to the left, 2 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 6 | Math Example--Geometric Transformation--Translating Triangles--Example 6TopicTransformations DescriptionThe triangle is translated 5 units to the right and 3 units up. The image includes both original and translated triangles, labeled ABC and A'B'C'. Example 6: "Draw the triangle that results from the following translation: 5 units to the right, 3 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 7 | Math Example--Geometric Transformation--Translating Triangles--Example 7TopicTransformations DescriptionA triangle is translated 4 units up and 5 units left, showing the original ABC and translated A'B'C' triangles. Example 7: "Draw the triangle that results from the following translation: 4 units up, 5 units left." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 8 | Math Example--Geometric Transformation--Translating Triangles--Example 8TopicTransformations Description
The triangle is translated 5 units up and 2 units right. The image shows both the original and translated positions of the triangle. Example 8: "Draw the triangle that results from the following translation: 5 units up, 2 units rogjt." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 9 | Math Example--Geometric Transformation--Translating Triangles--Example 9TopicTransformations DescriptionA triangle is translated 4 units to the right and 3 units down. The image shows both the original and the new triangle positions. Example 9: "Draw the triangle that results from the following translation: 4 units to the right, 3 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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MATH EXAMPLES--Teacher's Guide: Transformations | MATH EXAMPLES--Teacher's Guide: Transformations
This set of tutorials provides 56 examples of transformations of geometric figures on a graph. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Transformations and Definition of Transformations |
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MATH EXAMPLES--Transformations | MATH EXAMPLES--Transformations
This set of tutorials provides 56 examples of transformations of geometric figures on a graph. NOTE: The download is a PPT file. |
Applications of Transformations and Definition of Transformations |
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Promethean Flipchart: Geometry Applications: Transformations 1 | Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Transformations, Segment 1: Translations and Rotations]: https://www.media4math.com/library/geometry-applications-transformations-segment-1-translations-and-rotations This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-1-translations-and-rotations |
Applications of Transformations |
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Promethean Flipchart: Geometry Applications: Transformations 2 | Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Transformations, Segment 2: 3D Translations]: https://www.media4math.com/library/geometry-applications-transformations-segment-2-3d-translations This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-2-3d-translations |
Applications of Transformations |
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Promethean Flipchart: Geometry Applications: Transformations 3 | The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry. Note: The download for this resources is the Promethean Flipchart. The full video [Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry] can be found here: https://media4math.com/library/geometry-applications-transformations-segment-3-rotations-reflections-and-symmetry |
Applications of Transformations |
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Video Transcript: Geometry Applications: Transformations | Video Transcript: Geometry Applications: Transformations
This is the transcript for the video of same title. Video contents: In this program we look at applications of transformations. We do this in the context of three real-world applications. In the first, we look at translations and rotations in the context of roller coaster rides. In the second example we look at translations in three-dimensional space in the context of cargo ships. In the third example, we look at the design of observatories to look at rotations, reflections, and symmetry. |
Applications of Transformations |
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Video Transcript: Geometry Applications: Transformations, Segment 1: Translations and Rotations | Video Transcript: Geometry Applications: Transformations, Segment 1: Translations and Rotations
This is the transcript for the video of same title. Video contents: Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Applications of Transformations |
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Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations | Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations
This is the transcript for the video of same title. Video contents: Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations. |
Applications of Transformations |
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Video Transcript: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry | Video Transcript: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry
This is the transcript for the video of same title. Video contents: The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry. |
Applications of Transformations |
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VIDEO: Geometry Applications: Transformations | VIDEO: Geometry Applications: Transformations
In this program we look at applications of transformations. We do this in the context of three real-world applications. In the first, we look at translations and rotations in the context of roller coaster rides. In the second example we look at translations in three-dimensional space in the context of cargo ships. In the third example, we look at the design of observatories to look at rotations, reflections, and symmetry. |
Applications of Transformations and Definition of Transformations |
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VIDEO: Geometry Applications: Transformations, 1 | VIDEO: Geometry Applications: Transformations, Segment 1: Translations and Rotations.
Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. |
Applications of Transformations and Definition of Transformations |
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VIDEO: Geometry Applications: Transformations, 2 | VIDEO: Geometry Applications: Transformations, Segment 2: 3D Translations.
Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations. |
Applications of Transformations and Definition of Transformations |
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VIDEO: Geometry Applications: Transformations, 3 | VIDEO: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry.
The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry. |
Applications of Transformations and Definition of Transformations |
