Question

determine whether the figure has line, point, and/or rotation symmetry or no symmetry.
line
rotational
point
none (no symmetry)

Explanation:

Step1: Recall Symmetry Definitions

• Line Symmetry: A figure can be folded over a line so that the two halves match.
• Rotational Symmetry: A figure can be rotated by an angle (less than \(360^\circ\)) about a point and map onto itself.
• Point Symmetry: A type of rotational symmetry where the rotation angle is \(180^\circ\), meaning each point has an image directly opposite through the center point.

Step2: Analyze the Given Figure

The figure is two triangles intersecting at their vertices, forming a bow - tie - like shape (but with two triangles).

• Line Symmetry: If we draw a vertical line (or a horizontal line depending on the orientation) through the intersection point, folding the figure over this line will make the two triangles coincide. So it has line symmetry.
• Rotational Symmetry: If we rotate the figure by \(180^\circ\) about the intersection point, the figure will map onto itself. Since rotational symmetry includes \(180^\circ\) rotation (which is also point symmetry), it has rotational symmetry.
• Point Symmetry: As rotating by \(180^\circ\) about the intersection point maps the figure onto itself, it has point symmetry (because point symmetry is a special case of rotational symmetry with rotation angle \(180^\circ\)).

Answer:

• Line: \(\boxed{Checked}\)
• Rotational: \(\boxed{Checked}\)
• Point: \(\boxed{Checked}\)
• None (no symmetry): \(\boxed{Unchecked}\)

(Note: The figure has line symmetry (can be reflected over a line through the intersection), rotational symmetry (rotates \(180^\circ\) about the intersection point to map onto itself), and point symmetry (since \(180^\circ\) rotation about the intersection point (the center) maps each point to its opposite, so it has point symmetry as well).)