8.1+(winbr5)

Vocabulary
__Dilation__- A transformation in which every point //P// has an image point //P'// such that a line connecting the two poimts passes through a point O, known as the //center of dilation, and OP' = k x OP,// where //k// is the scale //factor// of the dilation. __Scale Factor__- In a transformation, the number by which the distance of the preimage from the center of dilation is multiplied to determine the distance of the image point from the center. __Center of Dilation__- The point in a dilation through which every line connecting a preimage point to an image point passes. __Contraction__- A dilation in which the preimage is reduced in size. __Expansion__- A dilation in which the preimage is enlarged in size.

Dilation in the Coordinate Plane

 * The distance from the orgin to the image of a point transformed by a dilation with the scalefactor n is n timesthe distance from the orgin to the preimage.
 * The image of a segment transformed by a dilation with a scale factor of n is n times the length of the preimage, and the slopes of the image and preimage are equal.

Example
//This picture is an example of what symbol DIlations look like.//


 * The formula to find the scale factor is D(x,y)=(4x,4y)**
 * the point that we are going to transform is (4,6)
 * image is the point D(4,6)=(4×4,4×6)=(16,24)
 * the scale factor is 4 because 4×4=16 and 6×4=24
 * Drawing Dilations**
 * Our point is on the top left of the triangle
 * The given scale factor is n, n=-1
 * As you can see in the picture each star moves 1 inch to the right
 * Dilations in a Coordinate Plane**
 * **A** || **OA** || **Scale Factor** || **Image, A'** || **OA'** || **Ratio OA'/OA** ||
 * **(6,8)** || 10 || **2** || (12,16) || 20 || 20/10=2 ||
 * **(6,8)** || 10 || **0.5** || (3,4) || 5 || 5/10=1/2 ||
 * **(6,8)** || 10 || **-1** || (-6,-8) || 10 || 10/10=1 ||
 * **(6,8)** || 10 || **n** || n×(6,8) || 10n ||  ||

http://regentsprep.org/Regents/Math/codilate/Ldilate.htm