Question

determine if the figure has line, point, and/or rotational symmetry
line symmetry
point symmetry
rotational symmetry
none of the above

Explanation:

• Line Symmetry: A figure has line symmetry if there's a line (axis) that divides it into two mirror - image halves. For this star - like figure with 6 arms (assuming the shape has 6 equal - looking parts), we can draw 6 lines (each passing through the center and the mid - point of an arm or the tip of an arm) that will split the figure into two congruent mirror - image parts. So it has line symmetry.
• Point Symmetry: Point symmetry is a special case of rotational symmetry (180 - degree rotation). If we rotate the figure 180 degrees around its center, each part of the figure will map onto another part. For example, the top arm will map to the bottom arm, and the left - side arms will map to the right - side arms appropriately. So it has point symmetry.
• Rotational Symmetry: A figure has rotational symmetry if rotating it by an angle less than 360 degrees around its center maps the figure onto itself. For this figure, the order of rotational symmetry (the number of times it maps onto itself as we rotate 360 degrees) is 6. The angle of rotation for symmetry is $\frac{360^{\circ}}{6}=60^{\circ}$. So rotating it by 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees, and 360 degrees (which is the same as 0 degrees) will map the figure onto itself. Thus, it has rotational symmetry.

Answer:

• Line Symmetry (checked)
• Point Symmetry (checked)
• Rotational Symmetry (checked)
• None of the above (unchecked)