Question

select all the correct answers.
what are the rotations that will carry this equilateral triangle onto itself?
225° clockwise rotation about its center p
270° counterclockwise rotation about its center p
90° counterclockwise rotation about its center p
240° clockwise rotation about its center p
200° counterclockwise rotation about its center p
120° counterclockwise rotation about its center p

Explanation:

Step1: Find the rotational symmetry of an equilateral triangle

An equilateral triangle has rotational symmetry of order 3. The formula for the angle of rotation \( \theta=\frac{360^{\circ}}{n}\), where \(n = 3\) (the number of sides). So \( \theta = 120^{\circ}\). Rotations that are multiples of \(120^{\circ}\) will map the equilateral triangle onto itself.

• For a \(240^{\circ}\) clockwise rotation: \(240\div120 = 2\), which is a multiple of \(120^{\circ}\).
• For a \(120^{\circ}\) counter - clockwise rotation: \(120\div120=1\), which is a multiple of \(120^{\circ}\).

Answer:

\(240^{\circ}\) clockwise rotation about its center \(P\), \(120^{\circ}\) counterclockwise rotation about its center \(P\)