In the Geometry, the points on the plane are defined by using a pair of Numbers and they are called coordinates.
Axis of SymmetryBack to Top
Now we will see types of symmetry.
There are three types of symmetry which are shown below:
x – Axis symmetry.
y – axis symmetry,
To find the axis of symmetry we have to follow some steps which are shown below:
Step 1: To find the axis of symmetry we take equation of figure.
Step 2: Then identify the coordinates of given expression.
Step 3: Now axis of symmetry can be found by using the formula shown below:
Axis of symmetry = -b/2a;
Step 4: Put the values in the given formula we get axis of symmetry.
Now we will understand these steps with the help of an example:
Suppose we have an expression y = x2 + 14x + 34 and we have to find the axis of symmetry.
To find the axis of symmetry we have to follow steps shown below:
Step 1: First we take an expression y = x2 + 14x + 34;
Then identify the coordinates of an expression:
Let a = 1, b = 14 and c = 34;
We know that the formula for finding the axis of symmetry is:
Axis of symmetry = -b/2a;
Put the value of ‘a’ and ‘b’ in the formula:
Axis of symmetry = -14/2 (1);
Axis of symmetry = -14/2;
So axis of symmetry is -7.
This is how we can find the axis of symmetry.
Axis of RotationBack to Top
On rotating the figures around its axis, we sometimes come to the situations where we find the figure looks exactly same as original figure. Then this point is called as point of rotational symmetry of the particular figure. Suppose we take a Circle, in circle, we say that centre of circle is the axis of rotation of circle. So we say that circle if rotated by any of the angle will be at the rotational symmetry.
This simply means that point about which the particular figure is rotated, then we say that it is the axis of the figure.
Now we will look at axis of rotation of Square. We observe that meeting point of two diagonals of square is the axis of rotation of square. It signifies that if we rotate the square about this point of rotation, we can find 4 positions where figure looks exactly same. Thus we conclude that square has the rotational symmetry of order 4. In order to find the angle of rotation of figure, we will divide the measure 360 degrees by the order of rotation.
Thus we conclude that angle of rotation of square will be equals to 360/ 4 = 90 degrees.
Axis of a SolidBack to Top
Each solid has its symmetry that is an axis along which if figure is rotated then it appears to be same. Axis of solid can be defined as an imaginary line passing through any solid about which or we can say around which a figure is symmetrical. Thus, axis of a solid is defined for every figure and it’s not mandatory that each figure has only one Axis of Symmetry it can be more than one and can be number of axes of symmetry.
Let us consider a cylinder, axis of symmetry in a cylinder can be considered as a line passing through center of cylinder crossing both ends of base, this line will be axis of symmetry as if cylinder is rotated along this axis then it appears to be same. That is along this axis, axis of rotation appears same. Similarly, a cube has also axis of symmetry but it has number of axes, that is a cube may possess different types of axes of symmetry that are, six 2 fold axes which appears as passing through midpoints of two opposite edges, second type is four 3 fold axes which pass through two opposite vertices and last type is of three 4 fold axes which is passing through two opposite vertices.
Thus, in total a cube can have 13 axes of symmetry. Similarly, a tetrahedron has seven axes of rotation or we can say axes of symmetry. An icosahedrons possess thirty one axes of symmetry and a Prism contains n + 1 axes of symmetry.