Question

do you know how?
find the number of lines of symmetry for each figure.
6.
7.
describe the rotational symmetry of each figure.
state whether each has point symmetry.
8.
9.

Explanation:

6.

• Line of symmetry: A line that divides a figure into two congruent parts.

For the arrow - like figure, there is \(1\) vertical line of symmetry.

• Rotational symmetry:

When rotated \(180^{\circ}\), the figure does not coincide with the original figure. So, the order of rotational symmetry is \(1\).

• Point symmetry:

A figure has point symmetry if for every point \(P\) on the figure, there is a point \(P'\) such that the center of symmetry is the mid - point of \(PP'\). This figure does not have point symmetry.

7.

• Line of symmetry:

For the crescent - like figure, there is \(1\) line of symmetry (the perpendicular bisector of the line segment joining the two endpoints of the arc - like shape).

• Rotational symmetry:

When rotated \(180^{\circ}\), the figure does not coincide with the original figure. So, the order of rotational symmetry is \(1\).

• Point symmetry:

This figure does not have point symmetry.

8.

• Line of symmetry:

This figure has \(1\) horizontal line of symmetry.

• Rotational symmetry:

When rotated \(180^{\circ}\), the figure coincides with the original figure. So, the order of rotational symmetry is \(2\).

• Point symmetry:

Since it has rotational symmetry of order \(2\) (rotation by \(180^{\circ}\) about a point maps the figure onto itself), it has point symmetry.

9.

• Line of symmetry:

This figure has \(3\) lines of symmetry (passing through each of the three “arms” and the center).

• Rotational symmetry:

When rotated by \(\frac{360^{\circ}}{3}=120^{\circ}\), the figure coincides with the original figure. So, the order of rotational symmetry is \(3\).

• Point symmetry:

When rotated \(180^{\circ}\), the figure does not coincide with the original figure. So, it does not have point symmetry.

Answer:

1. \(1\) line of symmetry; rotational symmetry of order \(1\); no point symmetry.
2. \(1\) line of symmetry; rotational symmetry of order \(1\); no point symmetry.
3. \(1\) line of symmetry; rotational symmetry of order \(2\); has point symmetry.
4. \(3\) lines of symmetry; rotational symmetry of order \(3\); no point symmetry.