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1. Explain what is meant by a rigid transformation.

2. Is the transformation below an isometry? Explain.

[pic]

3. The reflection image of [pic] in line q is [pic]. Find the measure of [pic] if [pic]

[pic]

4. Look at the arrangement of the sofa and chair in the room.

[pic]

Which room arrangement shows a translation of the arrangement above?

[A] [pic]

[B] [pic]

[C] [pic]

[D] [pic]

5. Name the image of [pic]DEF after reflection in lines [pic], in that order.

[pic]

6. What are the coordinates of the vertices when the figure is reflected in line m?

[pic]

[A] W´(5, 2), X´(–2, –4), Y´(–1, –2)

[B] W´(1, 2), X´(–2, 4), Y´(–5, –2)

[C] W´(5, –2), X´(2, –4), Y´(–1, 2)

[D] W´(2, 1), X´(4, –2), Y´(–2, –5)

7. Name the transformation. (Preimages are unshaded; images are shaded.)[pic]

8. Use the figure below.[pic]If segment x is reflected in the line y = x, its image is ________.

[A] segment q

[B] segment s

[C] segment r

[D] segment p

9. Rectangle KLMN is rotated 90[pic] clockwise about point O. Find the image of [pic].

[pic]

10. Which of the following is NOT true?

[A] A parallelogram has rotational symmetry and may have line symmetry.

[B] A triangle has rotational symmetry and always has line symmetry.

[C] A rectangle has rotational symmetry and always has line symmetry.

[D] A regular hexagon has rotational symmetry and always has line symmetry.

11. Which glide reflection could map figure ABC to figure [pic]

[pic]

[A] Translation: [pic]

Reflection: over the line [pic]

[B] Translation: [pic]

Reflection: over the line [pic]

[C] Translation: [pic]

Reflection: over the line [pic]

[D] Translation: [pic]

Reflection: over the line [pic]

12. Use the graph below to complete the sentence.

[pic]

Figure [pic] is the image of figure ABCD under a rotation _______

[A] [pic]about the origin.

[B] [pic]counterclockwise about the origin.

[C] [pic]counterclockwise about the origin.

[D] [pic]clockwise about the origin.

13. [pic] below is rotated clockwise [pic]about the origin. Find the coordinates of the vertices of the image [pic][pic]

14. Give the translation image of each of the following.

A. point [pic] B. [pic]

[pic]

15. The midpoint of [pic] is [pic]. One endpoint is [pic]. Find the coordinates of the other endpoint.

16. Segment [pic] is translated by the motion rule (x, y) [pic] (x – 4, y + 5).Find the coordinates of the endpoints of the image [pic]

[pic]

17. The point A(2, 5) is translated by the vector [pic] = [pic] and then reflected in the y-axis. Find the coordinates of its image, [pic]

18. Find the image of [pic]ABC after the glide reflection described.

Translation: [pic]; Reflection: in [pic]

[pic]

19. Graph the triangle whose vertices have the coordinates given below. Then draw its reflection in the x-axis.

(–6, 3), (–3, 3), (–6, 8)

20. Graph the figure with vertices [pic], [pic] [pic] and [pic] Draw the rotation image for a rotation of [pic] about the origin.

21. Find the image of [pic]ABC after the glide reflection described.

Translation: [pic]; Reflection: in [pic]

[pic]

22. If RS = 31 and QS = 74, find QR.

[pic]

[A] 105

[B] 31

[C] 33

[D] 43

23. Which of the following shows the image of [pic]ABC after the glide reflection described?

Translation: [pic]

Reflection: in [pic]

[A] [pic]

[B] [pic]

[C] [pic]

[D] [pic]

24. Let [pic] be between [pic] and [pic]. Use the Segment Addition Postulate to solve for [pic].

[pic] = [pic]

[pic] = [pic]

[pic] = 15

25. Find the distance between the points (–3, –5) and (–18, 3).

26. Solve for x:

[pic]

27. Solve for x:

[pic]

28. Name an angle complementary to [pic]

[pic]

[A] [pic]

[B] [pic]

[C] [pic]

[D] [pic]

29. Find the area:

[pic]

[A] [pic]

[B] [pic]

[C] [pic]

[D] [pic]

30. A play yard is 19 ft by 26 ft. A fence is to be built around the yard. How many feet of fencing will be needed? If fencing costs $5.45 per foot, what will be the cost of the fence?

Reference: [7.1.1.4]

[1] Every image is congruent to its preimage.

Reference: [7.1.1.5]

[2] No. It is not a rigid transformation.

Reference: [7.1.1.9]

[3] 3

Reference: [7.1.2.10]

[4] [A]

Reference: [7.2.1.11]

[5] [pic]MNO

Reference: [7.2.1.14]

[6] [B]

Reference: [7.2.1.18]

[7] Reflection

Reference: [7.2.1.24]

[8] [D]

Reference: [7.3.1.41]

[9] [pic]

Reference: [7.3.2.51]

[10] [B]

Reference: [7.5.1.75]

[11] [A]

Reference: [7.3.1.44]

[12] [B]

Reference: [7.3.1.46]

[13] P´(4, 5), Q´(0, 5), R´(0, 0)

Reference: [7.4.1.54]

[14] A. point I

B. [pic]

Reference: [1.5.1.56d]

[15] (–9, 5)

Reference: [7.4.1.57]

[16] A´(–3, 10); B´(1, 2)

Reference: [7.5.1.77]

[17] [pic](3, 2)

Reference: [7.5.1.71]

[18] [pic]

Reference: [7.2.1.13]

[19] [pic]

Reference: [7.3.1.42]

[20] [pic]

Reference: [7.5.1.72]

[21] [pic]

Reference: [1.3.1.25]

[22] [D]

Reference: [7.5.1.76]

[23] [D]

Reference: [1.3.1.26]

[24] [pic] = 6

Reference: [1.3.2.33]

[25] 17 units

Reference: [1.6.1.65]

[26] 3

Reference: [1.6.1.66]

[27] 2

Reference: [1.6.2.74]

[28] [D]

Reference: [1.7.1.81]

[29] [A]

Reference: [1.7.2.82]

[30] 90 ft; $490.50

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