Featured Image Caption: How to Find Axis of Symmetry
As you go to higher classes you will deal with multiple figures and objectives. The shapes and sizes will always differ amongst them. Each has a specific number of sides which you need to know. There is a basic way to sort these types of figures. You can draw a line exactly at its center to see the type. In case you can divide it perfectly into two halves, you can say these objects are symmetrical. There is a specific name for this line which is the axis of symmetry. Not all figures will have the same property if you draw this axis.
What are the Basic Types?
Not all types of symmetry will look the same if you study them. Translational symmetry is one of the most common types. Most of the symmetrical figures that you see fall in this category. No matter how far these objects are present from each other, they will look the same. Another common type of symmetry you can see is if you rotate the figures. Even after several rotations, the figure will retain a constant shape. A common example that you can see is the hexagonal shape. Be it left or right, the figure looks the same if you rotate.
A very common variety of symmetry is the objects that have a reflection. It is like something that you can cut into two equal parts. When you look at these parts, you will feel as if there is a mirror in between. For example, the letter ‘H’ has this exact property. If you put a line in between, the remaining two parts will be the same. There may be more than one line of symmetry for one individual figure. Hence to identify each of them, you need to use the common line of symmetry.
The Idea of Symmetrical Axis
First of all this line does not have any existence. It is an imaginary line that you have to just draw to see the characteristics of a figure. It can be in any direction and does not have a fixed angle. The basic function of this line is just like a plane mirror that you use at home. It allows you to fold the figure across the axis as well. That is why it has a lot of significance in graphs as well. Every straight line or figure has a graphical equation. Once you know that, you can find the axis of symmetry as well.
How to Derive One?
Here you have to know about the lines with the equation having degree 2. In general, the equation will look like ax^2 + bx – 1. When you see this type of equation, note down the values of a, b and c. For the x-axis, you just have to put the value (-b/2a). This is the formula that will directly give you the x-axis of the point. It is very simple to find the x-intercept of the axis when you know this process. After that just put this in the equation and you will get the ‘y’ part.
In schools, the maximum question comes from the chapter of a parabola. It has a complex equation that you will need to find the symmetrical axis. Once you find this line you can easily get the remaining points on the figure. The most important part of these lines is that it helps the viewer to see things. You get to see an object that has a perfect balance in space. Before you deal with the numerical part you have to understand the concepts and properties. Get tutorials of math classes from an interactive website called Cuemath.