Question

do the figures below have rotational symmetry? point symmetry? if a figure has rotational symmetry, give the smallest angle of rotation needed for the figure to appear unchanged. rotational symmetry?
○ yes
○ no
angle?
point symmetry?
○ yes
○ no
rotational symmetry?
○ yes
○ no
angle?
point symmetry?
○ yes
○ no

Explanation:

Step1: Analyze the first figure (cross)

A cross - shaped figure: To check rotational symmetry, we consider the angle of rotation. A cross can be rotated by \(90^\circ\), \(180^\circ\), \(270^\circ\) and \(360^\circ\) and still look the same. The smallest angle for rotational symmetry is \(90^\circ\) (since \(360\div4 = 90\), as it has 4 - fold symmetry). For point symmetry, a cross has point symmetry (rotating \(180^\circ\) around the center maps the figure onto itself), so the answer for point symmetry is "Yes".

Step2: Analyze the second figure (Y - shaped)

A Y - shaped figure: The Y - shape has 3 - fold rotational symmetry. The formula for the angle of rotational symmetry is \(\frac{360^\circ}{n}\), where \(n\) is the number of times the figure maps onto itself during a full rotation. Here \(n = 3\), so the angle is \(\frac{360^\circ}{3}=120^\circ\). For point symmetry, a Y - shaped figure does not have point symmetry (rotating \(180^\circ\) around the center does not map the figure onto itself), so the answer for point symmetry is "No".

Answer:

First Figure (Cross):

• Rotational Symmetry? : Yes
• Angle? : \(90^\circ\)
• Point Symmetry? : Yes

Second Figure (Y - shaped):

• Rotational Symmetry? : Yes
• Angle? : \(120^\circ\)
• Point Symmetry? : No