Exercise 38 Page 668

Let's begin by plotting the given vertices and drawing the figure on a coordinate plane.

We will determine whether it has line symmetry or rotational symmetry one at a time.

Line Symmetry

A figure in a plane has line symmetry if it can be mapped onto itself by a reflection in a line, called a line of symmetry. Notice that we can draw only one line in which our figure can be reflected so that it maps onto itself. Therefore, it has line symmetry.

Rotational Symmetry

A figure in a plane has rotational symmetry if it can be mapped onto itself by a rotation between $0^{\circ }$ and $360^{\circ }$ about the center of the figure — the center of symmetry. Unfortunately, there is no rotation that maps the given figure onto itself. Therefore, it has no rotational symmetry.