Level 2 · Intermediate ← Back to lesson

Symmetry: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

The rectangular outline has vertices $(-5,-2)$ , $(5,-2)$ , $(5,2)$ , and $(-5,2)$ . Does reflection across $y=x$ match it?

Answer choices for question 1 A Yes; any mirror through the center works B Yes; two of its sides have equal length C No; the image of (-5,-2) is absent from the outline D No; reflection changes its side lengths
2

A triangular outline joins $U(-2,1)$ , $V(4,1)$ , and $W(1,6)$ . Which fact establishes symmetry across $x=1$ ?

Answer choices for question 2 A It swaps U and V, fixes W, and pairs all three straight sides B It fixes W, which alone is enough C It passes through the midpoint of just one side, which alone is enough D It keeps every vertex fixed
3

A figure has least positive matching angle $36^\circ$ about O and finite rotational order. What is its order, including identity?

Answer choices for question 3 A 9 B 11 C 36 D 10
4

A figure has finite rotational order 6 about C, counting identity. How many of these matching rotations are nonidentity?

Answer choices for question 4 A 6 B 5 C 7 D 0
5

A square boundary centered at the origin has corners $(\pm5,\pm5)$ . The figure also includes four identical point marks. Three marks are at $(-4,1)$ , $(4,-1)$ , and $(2,3)$ . Where must the fourth be for point symmetry about the origin?

Answer choices for question 5 A $(-2,-3)$ B $(2,-3)$ C $(-3,-2)$ D $(0,0)$
6

For the exact block H outline shown, which tests succeed about its bounding-box center O?

Answer choices for question 6 A Only the vertical reflection B Only a quarter-turn C Both center-line reflections and a half-turn D A half-turn, but neither center-line reflection
7

The figure is a circle together with two identical marks at opposite ends of one diameter. The marks belong to the figure. What is its rotational order about O?

Answer choices for question 7 A 1 B 2 C 4 D Infinitely many
8

An unmarked square is changed by adding one point exactly at its center. The new figure includes both the boundary and that point. What happens to its rotational order about that center?

Answer choices for question 8 A It becomes 1 B It becomes 2 C It becomes infinite D It remains 4
9

A rectangle is centered at $(3,2)$ . A corner is $P(-1,-1)$ . What must its opposite corner be for the half-turn symmetry?

Answer choices for question 9 A $(1,1)$ B $(5,3)$ C $(7,5)$ D $(7,-5)$
10

A square's matching angles are recorded as $0^\circ$ , $90^\circ$ , $180^\circ$ , $270^\circ$ , and $360^\circ$ . What is the corrected count of distinct rotations?

Answer choices for question 10 A 5, because all recorded numbers differ B 4, because the first and last records are the same mapping C 3, because identity is forbidden D 2, because clockwise turns do not count
11

An unmarked square is turned 90 degrees clockwise about its center, then tested again from its original position with 90 degrees counterclockwise. Which test matches?

Answer choices for question 11 A Only clockwise B Only counterclockwise C Neither, since their directed angles differ D Both, since each turn maps corners and sides onto the square
12

A triangle is constructed by joining three points on a circle, equally spaced by $120^\circ$ turns about O. Which statement about its half-turn is correct?

Answer choices for question 12 A It fails, since a vertex lands between the three vertex directions B It succeeds because every triangle has point symmetry C It succeeds because the circle guide has point symmetry D It fails because a rotation changes the side lengths

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