1/12/16- Dilations on the Coordinate Plane

Warm-up

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Today we dealt specifically with dilations on the coordinate plane when the center of dilation is not on the origin.

Ex.) Dilate ∆GHI with G(3,1), H(6,7), and I(9,4) by a scale factor of 1/3 and center of dilation P(6,-2)

Before doing the problem, we need to agree on some ideas-

1.) Dilations with a center at the origin are easier problems, because all we need to do is multiply all coordinates by the scale factor, and we’re done!

2.) When the center is not the origin, we can’t just multiply the preimage points by the scale factor to get the answer.

There are three steps to such a problem:

1.) Translate all preimage points and the center of dilation such that the center of dilation is mapped to the origin [the point (0,0)]. This allows us to take advantage of dilations about the origin.

2.) Multiply all translated preimage points by the scale factor.

3.) Translate the dilated image back (the opposite directions of whatever you did for step 1)- this puts your image back to where it actually needs to be.

We went through the example with points above, and then students worked in their Springboard books: p. 241-245: 1-19

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