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6.7.1 Perform Similarity Transformations
Remember previous we talked about 3 types of CONGRUENCE transformations, in other words, the transformations performed created congruent figuresRotation, Reflection, and translationWe also discussed Dilations but not in great detail, now we will
A Dilation is a SIMILARITY transformation, in that by using a scale factor, the transformed object is similar to the original with congruent angles and proportional side lengths.REDUCTION VS ENLARGEMENTFor k, a scale factor we write (x, y) (kx, ky)For 0 < k < 1 the dilation is a reductionFor k > 1 the dilation is an enlargement
Let ABCD have A(2, 1), B(4, 1), C(4, -1), D(1, -1)Scale factor: 2Use the distance formula and SSS to verify they are similar
Usually the origin (if not re-orient)To show two objects are similar, we draw a line from the origin to the object further away, if the line passes through the closer object in the similar vertex then the objects are similar.
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