Saturday, 16 August 2008

Line Of Symmetry

In graph plotting, there is a property whereby the graph has symmetrical reflection over a special line. This is the "Line of Symmetry".

What I meant is explained below.

We will take an example to illustrate this special line.

Example: y = x2 + 2

This is a quadratic equation that can be easily plotted.
However, there is another "sister" equivalent to this equation.

Make x the target (instead of the function y)!

y = f (x) = x2 + 2 ==> x = f(y) = sqrt ( y - 2) using basic algebra to do it.

Let us now sketch the 2 graphs f(x) and f(y), and observe their features.

From the diagram above, you can see two graphs. One is the original y function or f(x), indicated as black line. The sister equation of f(x) is the f(y), indicated by the red line. They have the same shape except for the orientation!

They are reflections of each other. But the line of reflection is the diagonal blue dashed line in between them. The equation for this blue line is the basic y = x.

This blue line is termed the "Line of Symmetry".

This y = x line does not only apply to this example. It applies to any equation.


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