Monday, February 06, 2012

How do we identify transformations?

Geometry has been my weakest subject since I first entered high-school. The shapes and numbers along with letter that have no meaning behind them are annoying, and it's probably with that attitude why I am sitting here in Geometry class writing this blog. 
So lets get down to it so that I can get a good grade for this class. 

What is a transformation?
The best explanation I can give you about a transformation is that it's a movement or dilation (changing the size of) any shape on a coordinate plane. 

There are different ways to identify transformations, whether they be visually based off of an example, or mathematically where you have to go through the trouble of actually working the problem out. There are different types of transformations like reflections, rotations, translations and dilation. What exactly are these types of transformations?

Translations are the easiest of all the transformations, every point is moved a certain distance in a specific direction based on the coordinates given. This would be the kind of problem that would involve two triangles and one is a few inches away from the other. What you need to find is how far the triangle was moved from its original place on the coordinate plane and mark it. 
If you're one of the lucky high-school students you'll be given the translation change already and just have to make a new triangle using that distance given. 

Reflections are flipped figures that have a line of symmetry, meaning that they are (like the name states) reflections of the original. Easy peasy right?

The last two, rotations and dilation are a little harder to remember, mainly because they are as important in the geometric hierarchy. Sad. 

Rotations are turned around a single point while dilation is the change in size of a figure. 

With that said, we can now identify transformations and come up with one single definition for what a transformation is. Its the change of triangles using different methods that can be identified by their placement and symmetrical change on a plane. 

That wasn't so hard right? Right.

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