The axis of symmetry is a fictitious straight line that divides a shape into two identical parts, one of which is the mirror image of the other. When the two parts are folded along the axis of symmetry, they superimpose. The straight line is also known as the line of symmetry/mirror line.
This line can be horizontal, vertical, or slanted. This axis of symmetry can be found in nature, such as flowers, riverbanks, buildings, leaves, and so on. The Taj Mahal, India’s iconic marble structure, has an axis of symmetry that we can see.
What is the Axis of Symmetry?
In some places, the human face has a line of symmetry, but some faces are more symmetrical than others. In general, the term “symmetry” connotes balance. Symmetry can be used in a variety of contexts as well as situations. Symmetry is a fundamental concept in geometry that divides a figure into two halves that are exact reflections of one another.
Formula for Axis of Symmetry
The axis of symmetry formula is used to find the axis of symmetry of a parabola when applied to quadratic equations with the standard form of the equation and the line of symmetry. The axis of symmetry is a line that divides or bifurcates any object into two equal halves that are mirror images of each other.
This axis line, also known as the symmetry line, can be horizontal (x-axis), vertical (y-axis), or inclined (inclined). In geometry, a line of symmetry is a line that divides a geometric shape into two equal halves, resulting in a mirror image.
The axis of symmetry of a parabola is given by the formula,
x equals -b/2a for a given quadratic equation, y equals ax2 + bx + c
Where,
a and b are coefficients of x2 and x respectively.
c which denotes a constant term.
Example
Let’s solve an example for better understanding!
Find the axis of symmetry of the graph of y equals 2x2 + 8x – 3, using the formula.
Solution
Given,
y equals 2x2 + 8x – 3
Comparing the given equation with the standard form y equals ax2 + bx + c,
a equals 2, b equals 8, c equals -3
And the axis of symmetry is a vertical line; x equals -b/2a
Substituting the values of a and b,
x equals -8/2(2)
= -8/4
= -2
Therefore, the axis of symmetry is x is equal to -2.
Do Symmetry Lines Appear in Real Life?
In some places, the human face has a line of symmetry, but some faces are more symmetrical than others. The more symmetrical your face, the more beautiful it will appear. Supermodels and actresses are prime examples of this. The kidneys, lungs, and brain are other examples of human symmetry.
Radial symmetry can be found in starfish, sea anemones, jellyfish, and some flowers. Finally, plane or bilateral symmetry (also known as reflective symmetry) denotes the ability of a body to be divided into two equal halves that form mirror images of each other by a central (sagittal) plane.
Real-Life Examples of Symmetry
- Tree reflections in clear water and mountain reflections in a lake
- Most butterflies’ wings are identical on both the left and right sides
- Some human faces are identical on both the left and right sides
- A symmetrical mustache is also possible
Online Math Classes to Understand the concepts
Math Classes from Cuemath will help you understand the concept of symmetry in an easier way. It will help you grasp the topic in an easy way. Cuemath teaches children how to use reasoning to analyze and solve complex problems in its math classes. Another fundamental principle is conceptual learning, which is accomplished by introducing each math concept either through an activity or through pictorial models.
