1 A pentagon is translated down and to the left. How many sides does the resulting figure have?
A. 4
B. 5
C. It is impossible to determine without knowing how far the pentagon was translated.
D. 6
3. Which of the following capital letters results in the same letter over again when reflected about a horizontal line?
A. s
B. Y
C. D
D. A
4. A quadrilateral has vertices A, B, C, and D. A line of reflection is drawn so that A is 6 units away from the line, B is 4 units away from the line, C is 7 units away from the line, and D is 9 units away from the line. When quadrilateral ABCD is reflected about the line of reflection to create a new quadrilateral A′B′C′D′, which resulting point is closest to the line of reflection?
A. D’
B. b”
C. C’
D. A’
5. A pre-image arrow pointing east is rotated 135°° clockwise. In which direction is the image arrow pointing?
A. northwest
B. west
C. southwest
D. southeast
6. A point is rotated 272° clockwise. What is the equivalent smallest positive counterclockwise rotation?
7. What is the mapping notation that will transform triangle ABC to triangle A′B′C′?
A. (x−5,y−8)
B. (−y,x)
C. (x−8,y−5)
D. (−x,−y)
8. What is the mapping notation that will transform triangle ABC to triangle A′B′C′?
A. (y,−x)
B. (−y,x)
C. (x+2,y−14)
D. (x−4,y−8)
9. A rotation by how many degrees represents six full rotations?
10. What is true about the number of sides in any regular polygon that has at least one line of symmetry passing through two vertices?
A. The number of sides is a perfect square.
B. The number of sides is odd.
C. The number of sides is prime.
D. The number of sides is even.
15. Which of the following series of transformations is equivalent to reflecting about the line y=−x?
A. reflecting about the y-axis and then rotating 90° counterclockwise
B. reflecting about the y-axis and then rotating 180° counterclockwise
C. reflecting about the x-axis and then rotating 180°counterclockwise
D. reflecting about the x-axis and then rotating 90°counterclockwise
16. Which point maps to itself both when reflected about y=x and reflected about y=−x?
A. (0,0)
B. (−1,1)
C. (1,1)
D. (0,1)
17. True or false: Sequences of rigid motions can be applied to any type of polygon.
A. This statement is true.
B. This statement is false. Sequences of rigid motions can only be applied to polygons with fewer than 10 vertices.
C. This statement is false. No more than one rigid motion can be applied to any polygon.
D. This statement is false. Sequences of rigid motions can only be applied to convex polygons.
18. -True or false: A sequence of rigid motions that maps a pre-image to an image must contain no fewer than two unique rigid motions for the pre-image and the image to be congruent
A. This statement is false. If a sequence of rigid motions maps a pre-image to an image, the pre-image and the image are congruent no matter the details of the sequence of rigid motions.
B. This statement is true.
C. This statement is false. A sequence of rigid motions that maps a pre-image to an image must contain exactly two unique rigid motions for the pre-image and the image to be congruent.
D. This statement is false. A sequence of rigid motions that maps a pre-image to an image must contain no more than two unique rigid motions for the pre-image and the image to be congruent.
1. B (The number of sides does not change in a translation.)
2. Not provided
3. B (The capital letter Y is symmetric when reflected about a horizontal line.)
4. C (Because C is the point farthest from the line of reflection and its image will also be farthest from the line of reflection.)
5. A (The arrow will be pointing in the northwest direction after rotation.)
6. 88° counterclockwise (360 - (272 mod 360) = 88)
7. C ((x-8, y-5) will translate triangle ABC 8 units to the right and 5 units up.)
8. D ((x-4, y-8) will translate triangle ABC 4 units to the right and 8 units down.)
9. 60° (360° divided by 6 full rotations = 60°)
10. D (If a regular polygon has at least one line of symmetry passing through two vertices, then it must have an even number of sides by geometry principles.)
15. C (First reflecting about the y-axis will result in a 180° rotation, then reflecting about the x-axis and rotating 180° again will result in the same transformation as reflecting about the line y=-x.)
16. A (Point (0,0) is on the line y=x and y=-x, so it maps to itself when reflected about both lines.)
17. A (Sequences of rigid motions, such as translations, rotations, and reflections, can be applied to any type of polygon to preserve its shape and size.)
18. B (To map a pre-image to an image, there must be at least one rigid motion. However, it may require more than one rigid motion to achieve congruence between the pre-image and image.)