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:
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
Dilation Slide 23: Check out these sites: