Geometry 7.2a, Dilations & Similarity Transformations

An explanation of a dilation as a transformation that maps (x,y) to (kx, ky) where k is greater than 0, has a center at (0,0), and scale factor k. How similarity ratios are scale factors, drawing and describing dilations, how the pre-image and image of dilations are similar, similarity transformations, and finally determining whether polygons are similar.

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[JoAnnsSchool]

At 5:00 I accidentally referred to the squares as triangles. Sorry!

[mattrhoades]

Is it too advanced to talk about doing the last example in a single transformation?


Finding the center of the transformation (xc, yc) via intersection(m1*x + b1 = m2*x + b2) of any two lines formed from the pre-image to the corresponding points of the image (for example lines (y = mx+b) formed from segment AD and segment FB (using slope and intercept technique from prior classes) and then using the transformation D: ((x-xc), (y-yc)) -> (k(x-xc), k(y-yc)) where in this example xc = 15/2, yc = -3/2 and k = 3.


I know we have not covered handling a non "(0, 0)" center dilation yet and do not know whether that's coming up at any point in this class.


For those who read the comments, the D transformation I provide basically does a coordinate translation that puts the center of the dilation at 0, 0 in a new coordinate frame, does the dilation, and then puts its back into the original coordinate frame hence why both sides have (x-xc, y-yc) terms.


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