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9-12 Geometry Unit 1 Lesson 13

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Unit 1, Lesson 13

Incorporating Rotations

Geometry

Practice

Problem 1

Here are 2 polygons:

Select all sequences of translations, rotations, and reflections below that would take polygon \(P\) to polygon \(Q\).

<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 \(180^\circ\) around point \(A\).
Rotate \(60^\circ\) counterclockwise around point \(A\). Then reflect over the line \(FA\).
Translate so that \(A\) is taken to \(J\). Then reflect over line \(BA\).
Reflect over line \(BA\). Then translate by directed line segment \(BA\).
Reflect over the line \(BA\). Then rotate \(60^\circ\) counterclockwise around point \(A\).

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 \(P\) being transformed to Polygon \(Q\) 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 \(ABCD\) when translated by the directed line segment \(v\). Label the image of \(A\) as \(A’\), the image of \(B\) as \(B’\), the image of \(C\) as \(C’\), and the image of \(D\) as \(D’\).

<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 \(\ell\).

Plot 2 points \(A\) and \(B\) that stay in the same place when they are reflected over \(\ell\). Plot 2 other points \(C\) and \(D\) that move when they are reflected over \(\ell\).

<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 \(CAB\).
Construct the bisector of angle \(CBA\).
Construct the perpendicular bisector of \(BC\).
Construct the perpendicular bisector of \(AB\).
Construct the line perpendicular to \(AB\) through point \(C\).
Construct the line perpendicular to \(BC\) through point \(A\).

Problem 7

ForLesson 7: Construction Techniques 5: Squares

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

<p>Constructing a rhombus.</p>