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Symmetry - Definition, Types, Line of symmetry and Example

 

The word symmetry comes from the Greek word symmetria, meaning agreement in proportions or dimensions. Therefore, symmetry was used to denote the balance in beautiful and harmonious nature.

In geometry, the term symmetry denotes a shape or object divided into two identical parts.

Types of symmetry

  • Reflectional symmetry – When an object can be divided into two equal parts by a line of symmetry or a 3D plane, it is said to have reflectional symmetry.
  • Rotational symmetry – An object can be rotated about a fixed point or the line of symmetry in this type of symmetry
  • Translational symmetry – In this, the object can be translated or moved in a particular direction without changing its shape.
  • Helical symmetry – The object can be rotated and translated into a fixed axis of symmetry.
  • Scale symmetry – If an object does not change its shape when contracted or expanded, it is said to have a scaling symmetry
  • Glide reflection symmetry – An object is said to have glide reflection symmetry if a translation follows the reflection.
  • Rotoreflection – It is a combination of rotation and reflection.

Line of symmetry

A line of symmetry is an imaginary line by which the object or shape can be folded into two halves or appear like a mirror image. Different objects have a different axis of symmetry. 

For a parabola, the axis of symmetry is given by the formula, x=−b/2a for Quadratic Equation, y=ax2+bx+c where, a and b are coefficients of x2 and x respectively. c is a constant term.

Example

Find the axis of symmetry of the graph of y = 2x2 + 8x – 3, using the formula.

Solution

Given,

y = 2x2 + 8x – 3

Comparing the given equation with the standard form y = ax2 + bx + c,

a = 2, b = 8, c = -3

And the axis of symmetry is a vertical line; x = -b/2a

Substituting the values of a and b,

x = -8/2(2)

= -8/4

= -2

Therefore, the axis of symmetry is x = -2.

Points to Ponder

  • Symmetry is essential in every branch of science. Symmetry has its essence everywhere: biology, chemistry, physics, psychology, neuroscience, social interactions, art, architecture, photography, pottery, vessel making, carpets, rugs, aesthetics, and literature.
  • People find using symmetry as a powerful designing tool. Symmetrical designs look classy and organized. These days, photographers, graphic designers are also using the basic concepts of symmetry to enhance their work and presentations.
  • If you are ever wondering how to improve your artwork, try a little blend of symmetry in your work, and it will do wonders. One can apply the same concept in every field. Symmetry will also improve your writings and literature work.
  • Engineers of different fields can also apply symmetrical concepts to make unique designs. They can blend the concepts with artificial intelligence to create a masterpiece.
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