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9-12 Integrated Math 1 Unit 1 Lesson 13

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Unit 1, Lesson 13

Incorporating Rotations

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Integrated Math 1

Practice

Problem 1

Here are 2 polygons:

Select all sequences of translations, rotations, and reflections below that would take polygon to polygon .

<p>5-sided polygons, P and Q, on an isometric grid. Q is a transformation of P. P has vertices A, B, C, D, and E. Q has vertices J, A, F, G, and H.</p>

Rotate around point .
Rotate counterclockwise around point . Then reflect over the line .
Translate so that is taken to . Then reflect over line .
Reflect over line . Then translate by directed line segment .
Reflect over the line . Then rotate counterclockwise around point .

Problem 2

Flag semaphore is a way to use flags to signal messages. The diagram shows how to signal the letter Q. Describe a transformation that would take the left-hand flag to the right-hand flag.

<p>Stick-figure person with a square flag in each hand. Left-hand flag has an L. Right-hand flag an R. The right arm extends out horizontally from the body. The left extends upward at an angle.</p> — Q

Problem 3

ForLesson 12: Defining Translations

Match the directed line segment with the image of Polygon being transformed to Polygon by translation by that directed line segment.

<p>Congruent polygons. Polygon Q, translated right of Polygon P. No overlap, no touching edges.</p> — Translation 1

<p>Congruent polygons overlapping. Polygon Q, translated barely up and to the right of Polygon P. Left side of Polygon Q overlaps the right side of Polygon P.</p> — Translation 2

<p>Congruent polygons. Polygon Q, translated above and to the right of Polygon P. Bottom edge of Polygon Q touches the top edge of Polygon P.</p> — Translation 3

<p>Congruent polygons overlapping. Polygon Q, translated down and to the left of Polygon P. Top half of Polygon Q overlaps the bottom half of Polygon P.</p> — Translation 4

Translation 1
Translation 2
Translation 3
Translation 4

Problem 4

ForLesson 12: Defining Translations

Draw the image of quadrilateral when translated by the directed line segment . Label the image of as , the image of as , the image of as , and the image of as .

<p>Quadrilateral A B C D and directed line segment, v, on isometric grid.</p>

Problem 5

ForLesson 11: Defining Reflections

Here is a line .

Plot 2 points and that stay in the same place when they are reflected over . Plot 2 other points and that move when they are reflected over .

<p>Line L, with endpoints at the bottom left and top right</p>

Problem 6

ForLesson 9: Speedy Delivery

Here are 3 points in the plane. Select all the straightedge and compass constructions needed to locate the point that is the same distance from all 3 points.

<p>Three points, point A to the left of point B, point C above both points A and B.</p>

Construct the bisector of angle .
Construct the bisector of angle .
Construct the perpendicular bisector of .
Construct the perpendicular bisector of .
Construct the line perpendicular to through point .
Construct the line perpendicular to through point .

Problem 7

ForLesson 7: Construction Techniques 5: Squares

This straightedge and compass construction shows quadrilateral . Is a rhombus? Explain how you know.

<p>Constructing a rhombus.</p>