In this portion of our presentation, we are going to discover translations. First of all, what is a translation?
A translation is one of the transformations. It changes the location of the pre-image. Here's an example on paper:
A great example of using translations in real life is a level. The tool in the background is called a level. The level is a tool that tests if a surface is level or not, the bubble inside the glass tubes are very sensitive, if the surface that it's on is not even, the bubble will slide (translate).
Let's take a look at some other examples...
The next transformation we will discover is the Rotation.
A rotation changes the location and/or direction of the pre-image. A rotation happens when a something turns around a certain point.
A swivel chair is a great example of how rotations can make lives easier. The swivel chair rotates around the base rod of the chair which is the point of rotation. This allows the person sitting in the chair to move 360 degrees around. This is optimal movement and can allow for quicker movements in the office cubicle or workspace. That means that when you're working on that big project and need to grab a notepad, pencil, or stapler you can just swerve around to grab them.
3. Reflections (and symmetry)
Now, let's discover reflections and symmetry!
A reflection is a transformation that changes the direction and/or location of the pre-image.
That means that if a reflection happens, then the direction and/or location should change depending on the where the reflection line is residing.
Water is possibly the most beautiful example of how transformations can elegantly show up around us through nature (or man-made products). The image seen right now is breath-taking, and also a great example of reflections through water. The shore and horizon could be the reflection line, while the mountains and sky themselves would be the pre-image! There were other even more beautiful photos, but none of them had the perfect clarity of the reflection like this one...
Finally, we will discover dilations! So, what is a dilation?
A dilation is a transformation that changes the size of the pre-image.
That means that when the size of something changes while the shape and ratio are still maintained, it is known as a dilation. When you hear the word dilation, you might think of an eye dilating, which is correct. Since the eye's shape remains the same while growing or shrinking it's a dilation.
An example of dilations would be models o anything such as helicopters. Models of objects are a great example of how dilations are useful in real life. You can test the aerodynamics, balance et cetera, without needing to use or waste the actual object.
This photo here is just to prove that this indeed, is a dilation and not a similar shape, which we will discover later.
Let's check out some of the others...
These two cans of Coca Cola™ is a cute example of dilations appearing without us even noticing!
A similar shape is 2 shapes that have mainly the same shape (duh...) and dimension ratio, just a different size. It's pretty much a dilation in disguise.
This is an adorable example. It can also be taken as an example for a dilation, though it cannot be the EXACT same shape.