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Exam 22: Transformation Geometry

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Question 1

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Name the kind(s) of symmetry this figure has. (The dots mean it continues forever.)

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Question 2

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Complete each statement. A) The composition of ten different reflections and five different rotations could possibly be a _____ or a _____. B) A rotation always has _____ fixed point(s). (How many?) C) A translation with a vector 50 centimeters long can be expressed by the composition of two reflections, where the reflecting lines are (i) _____ centimeters apart, (ii) _____, and (iii) _____. D) If P' is the image of P for a clockwise rotation of 140° with center X, then key relationships tell us that _____ and _____. E) The composition of 200 reflections could be achieved most efficiently with _____ reflection(s).

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A) rotation; translation (in e...

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Question 3

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Joe and John were arguing about glide-reflections. Joe says that the order that you do the steps of a glide-reflection makes a difference in your answer. John says that it doesn't. Who is correct about whether the order matters? Why? (What was done wrong?)

For each pair of figures, determine which single-step transformation might take the shaded figure to the other. If a rotation, find the center and angle of rotation. If a reflection, show the line of reflection. If a translation, give an arrow (vector). a. b. c . A) $\underline{\quad\quad}$ B) $\underline{\quad\quad}$ C) $\underline{\quad\quad}$

A) Show the image of shape S for the composition given by (reflection in m)° (translation with vector v). B) What single type of rigid motion accomplishes the same thing as the composition in part A?

Select "same" or "reversed" for each item listed in the chart. $\begin{array} { | l | l | } \hline \text { Type of rigid motion } & \text { Clock orientation of image compared } \text { with original } \\\hline \end{array}$ $\begin{array} { | l | l l | } \hline \text { A) Reflection}\quad\quad\quad & \text { A) same \quad reversed } \\\hline \text { B) Rotation } & \text { B) same \quad reversed } \quad\quad\quad\quad\quad\quad\quad\\\hline \text { C) Translation } & \text { C) same \quad reversed } \\\hline \text { D) Glide-reflection } & \text { D) same \quad reversed } \\\hline\end{array}$

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Find the missing information. (Drawing is alright. If your drawing is "off," write words to communicate your intent.) A) Missing: the vector for this translation B) Missing: the angle and direction for this rotation

See below. The unlabeled figure at top left is the original figure. Each of the others, labeled a-h, is the result of a rigid transformation of the original. Determine if each is the result of a translation, rotation, reflection, or glide-reflection.

Which of the following would be more valuable if you could have only one of them (and composition)? (Hint: theory) A) all possible rotations and translations B) all possible reflections

Complete each statement. A) The composition of 15 reflections in different lines with 13 rotations with different centers might be a _____ or a _____. B) A reflection has _____ fixed point(s). (How many?) C) If two polygons are similar with a scale factor of 2, then a 20° angle in the smaller polygon will correspond to an angle of _____ in the larger polygon.

"Figure X is congruent to Figure Y." What does that statement mean?

Name the type of rigid motion involved in each of the listed motions. Take into account the different types of "eyes."

Complete each of the following motions, being careful to fit your answer to the grid. A) reflection B) translation C) glide-reflection

Complete the chart. $\begin{array} { | l | l | } \hline \text { Type of rigid motion } & \begin{array} { l } \text { In addition to the original figure, what needs to be } \\\text { given in order to do the rigid motion? }\end{array} \\\hline \text { A) Reflection } & \text { A) } \\\hline \text { B) Rotation } & \text { B) } \\\hline \text { C) Translation } & \text { C) } \\\hline \text { D) Glide-reflection } & \text { D) } \\\hline\end{array}$

For the figures below, what single type of motion would accomplish each?

A) Give the final image of X for (translation, vector v)° (reflection in line m). B) Name the single rigid motion equal to the composition in part A. You do not have to give all the important information, just the type of motion. (translation, vector v)° (reflection in line m) is a _____.

Two lines intersect at point Q, making an angle of 60°. What single rigid motion equals the composition of reflections in those two lines? Describe this single rigid motion as completely as you can from the given information.

Name three types of rigid motions.

Accurately draw each of the following. A. the vector for this translation B. the line of reflection involved here