Translations, Rotations, and Reflections

Coordinate Graphs use ordered pairs to plot different shapes and designs.  One way we use coordinate graphs is to move shapes around to different parts of the graph through translations, rotations, and slides.

This is used in the real world by computer programmers to make models and animations.   

Try your skill at using translations, rotations, and
slides by clicking on this link for a Khan Academy Simulation.  Transformations Computer Practice  

Transformations are a general term that means that things are being moved around in the coordinate graph.  

Here are some terms that you probably know already:  slides, flips, and turns.

• Slides- when an object is moved without lifting it off the page is a slide.  Another way of saying slide is a translation.  Translations can be found by using an equation like (x + 2, y - 1).  For example, if the original point in an ordered pair (x,y) is (4,1)  then the translation of that point would be (4+2, and 1-1) or  the new point would be at (6,0). 
• Flips-  another word for a flip is a reflection.  The reflection of the object is when it is "flipped" on the opposite side of the x or y axis.   One way to do the reflection of a shape in an ordered pair (x,y) is to multiply either the x or y by negative 1.   Let's say for instance that we want to flip a point over the x axis. Using point (3, 2) we would multiply the x coordinate 3 by -1.  The new point would be at (-3,2) 
• Turns-   turning an object around from a center point is yet another way we can move the object.       A Rotation is another name for a turn because there is a center point that remains the same as the shape rotates on 1 point.  Both the size of the figure and the distance between the points remains the same as the figure rotates to different quadrants.                                                                                                                  

Here's a video link that shows how to rotate a quadrilateral 90 degrees and a way to predict where the new points will be on the coordinate graph.  Rotations of 90 Degrees Video

Online Quiz for Transformations: Translations, Reflections, and Rotations.