A dilation centered at point C with a scale factor of k, where can be defined as follows: 1. The image of point C is itself. That is, _____ 2. For any point P other than C, the ____________________________
NOTE: If, then the dilation is a ____________ If, then the dilation is an ____________
Example: Line segment AB with endpoints A(2, 5) and B(6, -1) lies in the coordinate plane. The segment will be dilated with a scale factor of and a center at the origin to create. What will be the length of ?
Example: Under a dilation of scale factor 3 with the center at the origin, what will be the coordinates of the image of point A(3, 4)? point B(4,1)? What do you notice about the coordinates of points A and A’ as well as B and B’ in relation to the scale factor?
Theorem: If the center of dilation is the origin and the scale factor is k, the coordinates of the point A’, the image of A(x, y), will be __________.