Question: Describe the turn symmetries of a right isosceles triangle.
Answer Choices:
A. Rotation by exactly θ° about any vertex
B. Rotation by exactly θ° about point of intersection
C. Rotation by any integer multiple of 120° about the point of intersection
D–G. (Other rotation-related options)
Answer: None of the given choices are correct. Correct answer should be:
Rotation by exactly 180° about the midpoint of the hypotenuse
Question: If I have a point and its image, is that enough to determine the type of transformation used?
Answer Choices:
A. No, any of the motions could work.
B. Yes, only a reflection.
C. Yes, only a glide reflection.
D. Yes, only a rotation.
E. Yes, only a translation.
Answer: A. No, because with a single point and an image, any of the types of motion could work.
Question: Describe the turn symmetries of half a circle with its diameter.
Answer Choices:
A–G (various angles and centers of rotation)
Answer: D. Rotation by exactly 180° about the midpoint of the diameter clockwise only
Question: Which of the letters J, O, B, H, L, P, R, Q, A, and I are their own images under a rotation by an angle whose measure is less than 360°?
Answer Choices:
A. O, H, A, I
B. None of the letters are their own image under a rotation by an angle whose measure is less than 360°
Answer: A. O, H, A, I
Question: Describe how to construct the center of a given circle if the center is not marked.
Answer Choices:
A. Pick any three points A, B, and C…equilateral triangle.
B. Pick four points…
C. Pick any two points…
D. Pick any three points A, B, and C…construct the perpendicular bisectors of AB and AC…
Answer: D
Question: Sammi said every reflection is a rotation. How do you respond?
Answer Choices:
A. Sammi is correct. A reflection is a rotation when α is 180°.
B. Sammi is incorrect; full-plane comparison is needed.
C. Sammi is incorrect. A reflection is a rotation only when α is 90°.
D. Sammi is correct. Every reflection is a rotation.
Answer: B. Sammi is incorrect. To determine if the motions are equivalent, one has to consider the entire plane. The orientations are different.
Question: With an appropriate font, the image of 1881 is 1881 after reflection in either a horizontal or vertical line.
Answer Choices:
(Not multiple-choice)
Answer: True. The number 1881 is a reflectional (ambigram) palindrome in this case.
Question: Noah says any image under a half-turn can also be achieved by a translation. How do you respond?
Answer Choices:
A. Not true for any figures.
B. True for a circle, not for all figures.
C. True for all figures.
D. True for all figures (with rectangle example).
Answer: B. This is true for a circle but not for all figures.
Question: Given any point with the coordinate (h, k), what are the coordinates of the image of the point under a half-turn about A(0,5)?
Answer Choices:
(Not multiple-choice; concept-based)
Answer: The image is (−h, 10−k)
Question: List several figures other than rectangles that tessellate the plane using translations.
Answer Choices:
A. Trapezoid
B. Puzzle shape
C. Hexagon
D. Triangle
E. Parallelogram
Answer: B, C, D, E