Geometry help can be hard to find, but we are here to help! 
In this lesson, we are going to describe a topic in geometry that I know was frustrating for myself to understand fully.  The topic is Transformation Geometry.  Transformation geometry is a name for the pedagogic theory for teaching Euclidean geometry using dilations, rotations, reflections, and translations to move a graph throughout the x and y axis. 

The word Transform simply means to change.  We will be changing the position of a line or shape around the coordinate plane using the basic transformations of flip, slide, and turn.

For these problems it’s important to, if possible, graph the line or shape.  This will allow a visualization of the shape for easier transformation and give you some geometry help.



Flip or Reflection:

A reflection is when a shape is flipped across either the x axis or the y axis in the opposing direction.  Basically, the idea is to mirror the image.

Here is our beginning graph:



This is a graph of 3 points forming a semi-triangle.  The 3 points are located at (2,4) (3,6) and (5,3).  We are going to FLIP it now over the Y axis. 

Here is our graph after the flip:

Since we flipped it over the y axis, simply reverse the x values to find our new graph!
In this case our new points are (-2,4) (-3,6) and (-5,3)




Translation or Slide:

Here we are going to take the full object or line and just move it in a direction without losing its shape.  In the problems, they will tell you which direction you will move in.  We will use our same graph from the Flip example to show the difference:



Now we are going to take our shape and SLIDE it down 2 and left 3.  Essentially, every x value will be decreased by 3 and every y value will be decreased by 2.




So now our new points are located at (-1, 2) (0,4) and (2,1).
The graph looks slightly different, but this is due to the x axis value sizing.  The graph is exactly the same except down 2 and left 3.




Rotation or Turn:

With rotations we are going to turn the shape pivoting off 1 direct point either left or right.  Picture the hands of a clock turning around a pivot point.  Don’t worry we are here for all your geometry help needs.  Here is an example beginning graph:





Now we are going to rotate the line 90 degree left using the point (0,4) as a pivot point.  Basically picture 0,4 being the middle of your watch and the minute hand rotating counterclockwise.



While originally our points were (0,4) (2,4) (4,4) and (6,4)
We now ROTATED our line counterclockwise using (0,4) as a pivot point.
Now our points are (0,4) (0,6) (0,8) and (0,10).