Flip, Slide or Turn?

Our study of horizontal, vertical and diagonal would not be complete without recognizing that there are ways to move a shape to another orientation or position. This process is called TRANSFORMATION. There's a genre of popular children's toys called Transformers. They do flips, slides and turns. Let's see what those words mean.

We call these moves by special names, and they follow agreed-upon rules, so all of us who modify a shape can do so in a repeatable fashion. Why bother? Because mathematicians (people) like consistency.

If I ask you to create a right triangle:

• of a certain size
• with the right angle to the right side and the hypotenuse at the top
• using 1 point black lines
• fill the figure with green
• slide it 2 inches to the right
• rotate it 90 degrees

I want your work to look like the figure to the extreme right. The red dots are there to indicate a point of rotation. The line shows the "hinge" about which it is reflected

You might be doing this with pencils. No problems for you, especially if you have an eraser!

Or you might have software, like the Adobe Illustrator program I use to create Excel Math problems. If you use software, you'll be hunting around the menus frantically wondering what to do. The process to follow goes like this on my machine:

1. Create a triangle by using the polygon shape tool set to 3 sided-figure. Click and there it is!
2. Move the vertices around to get the right triangle shape you want.
3. Fill with Mint Julep Green (I can't match that green with browser-friendly Internet text colors).
4. Click and Drag (slide/move) it to the right.
5. Go to the palette (menu) and select Object/Transform/Rotate and enter 90, press ENTER

To read more about flips, slides and turns, visit our April 30, 2012 blog post and download a free math worksheet. These are the transformations we teach to elementary school kids in math class. There are others.

For example, shear slants things. Scale changes the size. Transform each lets you select whether to change angles, size in vertical or horizontal directions, etc.

Finally, although these are plane figures (on a flat surface) we can still arrange them in "vertical space" or layers. That involves some instructions regarding whether to put this shape in front, middle, back, etc.