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9-12 Integrated Math 1 Unit 1 Lesson 18

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K-5 Math 6-8 Math •9-12 Math

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•Integrated Math 1 Integrated Math 2 Integrated Math 3

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 •Lesson 18 Lesson 19

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Lesson 18

18.1 Warm-up 18.2 Activity 18.3 Activity Student Lesson Summary

Unit 1, Lesson 18

Practicing Point-by-Point Transformations

$Course Icon$

Integrated Math 1

18.1

Warm-up

Obstacles

Describe the transformations needed to get through the maze.

Are You Ready for More?

18.2

Activity

Obstacle Course

Standards Alignment

Building On

Addressing

G-CO.2

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

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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.

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Building Toward

For each diagram, find a sequence of translations and rotations that take the original figure to the image so that if done physically, the figure would not touch any of the solid obstacles and would not leave the diagram. Test your sequence by drawing the image of each step.

Take to .
Take to .

18.3

Activity

Point by Point

Standards Alignment

Building On

8.G.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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Addressing

G-CO.2

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

View Full Standard

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.

View Full Standard

For each question, describe a sequence of translations, rotations, and reflections that will take parallelogram to parallelogram .

Student Lesson Summary

Sometimes it's not hard to figure out a transformation that takes all the points of one figure directly to all the points of its image. Here, it looks like there is a 90-degree rotation that will take figure to figure . It is not obvious where the center of rotation would be though.

<p>Two congruent quadrilaterals labeled A B C D and E F G H.</p>

Instead, we could describe the transformation in two steps. First, translate figure by the directed line segment . Next, rotate the image of clockwise by angle using center . It looks like this is a 90-degree rotation, but we can be sure the rotation will work if we use the labels to define the rotation instead of an angle measure. This method of matching up one point at a time until the whole figure has been taken to the image will work for any transformation, including ones in which it's hard to see a single transformation from one figure to the other.

Glossary

None

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Standards Alignment

Building On

Addressing

Building Toward

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.

View Full Standard

Are You Ready for More?

Are You Ready for More?

Building Toward