Slide 1:Geometry: Math 8


Slide 2:To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn about include: Translation Rotation Reflection Dilation


Slide 3:A translation "slides" an object a fixed distance in a given direction.  The original object and its translation have the same shape and size, and they face in the same direction. Translations are SLIDES.


Slide 4:Let's examine some translations related to coordinate geometry.   The example shows how each vertex moves the same distance in the same direction.


Slide 5:In this example, the "slide"  moves the figure7 units to the left and 3 units down.


Slide 6:A rotation is a transformation that turns a figure about a fixed point called the center of rotation.  An object and its rotation are the same shape and size, but the figures may be turned in different directions.


Slide 7:The concept of rotations can be seen in wallpaper designs, fabrics, and art work.


Slide 8:This rotation is 90 degrees counterclockwise.


Slide 9:A reflection can be seen in water, in a mirror, in glass, or in a shiny surface.  An object and its reflection have the same shape and size, but the figures face in opposite directions.  In a mirror, for example, right and left are switched.


Slide 11:The line (where a mirror may be placed) is called the line of reflection.  The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection. A reflection can be thought of as a "flipping" of an object over the line of reflection.


Slide 12:A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation used to create an image larger than the original is called an enlargement.  A dilation used to create an image smaller than the original is called a reduction.


Slide 13:Dilations always involve a change in size. Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (x2).


Slide 14:REVIEW: Answer each question……………………….. Does this picture show a translation, rotation, dilation, or reflection? Rotation


Slide 15:Does this picture show a translation, rotation, dilation, or reflection? Dilation


Slide 16:Does this picture show a translation, rotation, dilation, or reflection? (Line) Reflection


Slide 17:Which of the following lettered figures are translations of theshape of the purple arrow?  Name ALL that apply. Letters a, c, and e are translations of the purple arrow.


Slide 18:Has each picture been rotated in a clockwise or counter-clockwise direction? The birds were rotated clockwise and the fish counterclockwise.


Slide 19:Basically, a tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping and no gaps.


Slide 20:Dutch graphic artist M. C. Escher (1898-1972) is known for his creative use of tessellations in his work. What transformations can you see in this picture? The birds and fish have been translated here.


Slide 21:What transformations can you see in this Escher print? Some birds have been translated and some have been rotated.


Slide 22:Can you name examples in real life of each transformation? Translation Rotation Reflection Dilation


Slide 23:Check out these sites: http://www.farraguttn.com/fhs/math/nctm/index.htm http://www.mathsnet.net/transformations/index.html http://www.mcescher.com/