Geometry | Unit 1 | Lesson 13: Incorporating Rotations | Practice Problems

Here are 2 polygons: Select all sequences of translations, rotations, and reflections below that would take polygon \(P\) to polygon \(Q\).

• Rotate \(180^\circ\) around point \(A\).

• Rotate \(60^\circ\) counterclockwise around point \(A\) and then reflect over the line \(FA\).

• Translate so that \(A\) is taken to \(J\). Then reflect over line \(BA\).

• Reflect over line \(BA\) and then translate by directed line segment \(BA\).

• Reflect over the line \(BA\) and then rotate \(60^\circ\) counterclockwise around point \(A\).

The semaphore alphabet is a way to use flags to signal messages. Here's how to signal the letter Q. Describe a transformation that would take the left hand flag to the right hand flag.

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Match the directed line segment with the image of Polygon \(P\) being transformed to Polygon \(Q\) by translation by that directed line segment.

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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 \(D’\).

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Here is a line \(\ell\). Plot 2 points, \(A\) and \(B\), which stay in the same place when they are reflected over \(\ell\). Plot 2 other points, \(C\) and \(D\), which move when they are reflected over \(\ell\).

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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.

• 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 a line perpendicular to \(AB\) through point \(C\).

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

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