Write three capital letters of the English alphabet which have neither rotational symmetry nor reflection symmetry.
The correct answer and explanation is:
The correct answer is F, G, J.
To understand this, it is important to define two types of symmetry:
- Rotational Symmetry means a figure looks the same after being rotated by a certain angle less than 360 degrees around a central point.
- Reflection Symmetry means a figure can be divided into two identical halves that are mirror images of each other along a line of symmetry.
Now let us examine why the letters F, G, and J have neither type of symmetry.
F does not have reflection symmetry. There is no vertical or horizontal line that divides it into mirror-image halves. It also lacks rotational symmetry. If rotated 180 degrees or any other amount less than a full turn, it does not resemble its original position.
G has a curved shape and an open end on the right, which breaks both symmetry types. It does not have reflection symmetry because its left and right sides are not mirror images. It also does not have rotational symmetry, as turning it does not create a matching image in any position before 360 degrees.
J is also asymmetrical. It has a long straight line on one side and a curve at the bottom. Reflecting it either vertically or horizontally does not produce a mirror image. Rotating the letter changes its orientation and does not result in a match with its original form.
These three letters are unique in that they break both kinds of symmetry, unlike many other capital letters. For instance, the letter A has vertical reflection symmetry, and the letter N has rotational symmetry of 180 degrees. Letters such as H, I, and O exhibit both reflection and rotational symmetry. F, G, and J stand out because they have neither, which makes them ideal examples for this question.