Chapter 14.8, Problem 12CE

(a)

To determine

To find: The translational symmetry of the pattern.

Answer to Problem 12CE

The pattern is not a translational symmetry.

Explanation of Solution

Given information:

The given pattern design is shown below.

  

Calculation:

A design can also have translation symmetry if there is a translation that maps the figure onto itself.

Translational symmetry occurs only in pattern that cover a plane. But the given pattern is asymmetrical in nature so it is not a translational symmetry.

Therefore, the pattern is not a translational symmetry.

(b)

To determine

To find: Line symmetry of the pattern.

Answer to Problem 12CE

The given pattern is not a line symmetry.

Explanation of Solution

Given information:

The given pattern design shown below.

  

Calculation:

The line of symmetry is the imaginary line where fold the image and have both halves match exactly.

In the above pattern draw a line of axis then fold along that line the parts of object sides of the line not exactly coincide.

Hence the given pattern is not a line symmetry.

Therefore, the given pattern is not a line symmetry.

(c)

To determine

To find: Point symmetry of the pattern.

Answer to Problem 12CE

The pattern is not a point symmetry.

Explanation of Solution

Given information:

The given pattern design shown below.

  

Calculation:

Point symmetry occurs when there exists a point on an object that splits the object into two parts in which each part has a matching part the same distance from the central point, and face different directions.

The given pattern is asymmetrical in nature , therefore the pattern is not a point symmetry.

Therefore, the pattern is not a point symmetry.

(d)

To determine

To find: The rotational symmetry of the pattern.

Answer to Problem 12CE

The pattern is not a rotational symmetry.

Explanation of Solution

Given information:

The given pattern design is shown below.

  

Calculation:

A shape has a rotational symmetry when it still looks the same after some rotation.

The given pattern is not symmetry if rotated because the shape is asymmetrical.

Therefore, the pattern is not a rotational symmetry.