The entire universe follows the concept of symmetry and people can very easily find this particular concept into day to day objects in daily life whenever they will cut any shape into two identical parts. So, the imaginary line which will be dividing any kind of shape into two identical parts will be known as the concept of the axis of symmetry. Whenever a square will be folded along the diagonal it will help in creating the mirror image of itself and this particular concept will be based upon the concept of the axis of symmetry. Similarly, the rectangle will always have two axes of symmetry and any other kind of polygon will have an axis of symmetry which will depend upon the number of sides possessed by it.
The basic properties of the axis of symmetry are:
• Whenever the object will be cut through the axis of symmetry it will help in creating the mirror image of itself
• Whenever the object will be rotated around the axis of symmetry by a certain angle it will look the same and cannot be distinguished before as well as after rotation throughout the process.
• It can be either horizontal, vertical, slanting but will always be straight.
This axis of symmetry of circle has been explained as:
The circle will be having an infinite axis of symmetry and for this particular purpose, people need to take into consideration the shape of a circle with a Centre at O so that any number of straight lines can be perfectly drawn through the passing of the centre and these will be known as the diameter of the circle. The diameter of the circle will be dividing the circle into two equal and congruent parts so that there will be an infinite number of diameters and hence there will be an infinite number of axes of symmetry as well. Circle also comes with the concept of rotational symmetry because people can very easily rotate the circle around the centre without any kind of doubt in the whole process.
The axis of symmetry of the parabola has been explained as:
Parabola can be easily divided into two similar parts along one line only and this will be known as the line of symmetry. It can be right, left-facing, horizontal or vertical and also helps in determining the type of parabola very successfully throughout the process. Similarly, this particular process can be right facing or left facing and will further make sure that everything will be undertaken through the vertex without any kind of problem.
Axis of symmetry equation has been explained as:
For all the parabola which has symmetry as vertical, the equation will be passing through the X intercept and similarly for all the parabola whose axis of symmetry is horizontal the equation will be passing through the Y-intercept throughout the process.
Axis of symmetry formula can be categorised into two main options which are explained as follows:
• Standard form: In this particular case the quadratic equation will be given by Y =AX squared + BX + C where A and B will be the coefficients and the formula will be X = minus B/2A.
• Vertex form: In this particular case the quadratic equation will be given by Y =A into X – H whole square + K where H and K are the coordinates of the vertex of the parabola. The axis symmetry will be lying on the same line which will be H = minus B/2 a.
Hence, depending upon the right kind of classes from the house of Cuemath is the best possible approach of having a good hold over the basic technicalities of this particular topic so that everybody can score good marks in the exam.