Question

question 9 of 25

a line has ________ rotational symmetry.

a. seven-fold
b. six-fold
c. four-fold
d. two-fold

Explanation:

Define rotational symmetry of a line

A geometric figure has rotational symmetry if it can be rotated about a central point by an angle of less than \(360^\circ\) and still look exactly the same as the original figure. The order of rotational symmetry (or fold symmetry) is the number of times the figure maps onto itself during a full \(360^\circ\) rotation.

Analyze the rotation of a line

Consider a straight, infinite line. If we select any point on the line as the center of rotation:

1. Rotating the line by \(180^\circ\) (a half-turn) maps the line directly back onto itself.
2. Rotating the line by \(360^\circ\) (a full-turn) also maps the line back onto itself.

Determine the fold symmetry

Since there are 2 positions within a full \(360^\circ\) rotation where the line maps onto itself (\(180^\circ\) and \(360^\circ\)), a line has two-fold rotational symmetry.

Answer:

• A. seven-fold
• B. six-fold
• C. four-fold
• D. two-fold (Correct answer)