Download Fundamentals of Geometry with Examples - Study Guide | MATH 135 and more Study notes Geometry in PDF only on Docsity! Math 135 Section 9.2 Similitudes and Similarity Size transformations Let O be the center of the size transformation and k be the scale factor. The image of any point A under the size transformation with center O and scale factor A′where: 1) A′ is on ray OA 2) k OA AO = ′ Example 1 On the square lattice portions shown, find the image of OA under the size transformation with center O and a scale factor of 2=k a) A O To find the image of B, we extend AB through B and mark off B′where ( )ABBA 2=′ A' A O b) B O Solution: B' B O Example 4 Find the image of ABCΔ under the size transformation with center O and a scale factor of 2=k B C A O Extend the following segments from the center O ( )OBBOwhereBO 2 1 =′′ ( )AOAOwhereAO ′=′′ 2 1 ( )OCCOwhereCO 2 1 =′′ A' B' C' B C A O Example 5 Determine if ''' CBAΔ is a size transformation image of ABCΔ for )4,1(A′ , )4,7(B′ , )1,4(C ′ )1,2(A , )1,6(B , and )1,4( −C . If yes, find the center of rotation and the scale factor. If no, explain why not. 4 2 -2 -5 5 C(4,-1) A(2,1) B(6,1) C'(4,1) B'(7,4)A'(1,4) Find the center of rotation by extending lines through AA′ , BB′ ,and CC ′ . The point of intersection of these points will be the center. 4 2 -2 -4 -6 -5 5 (4,-5) C(4,-1) A(2,1) B(6,1) C'(4,1) B'(7,4)A'(1,4) The scale factor would be: 2 3 = ′′ = ′′ = ′′ = AC CA BC CB AB BAK Properties of Size Transformations 1) Size Transformations take lines to lines, rays to rays, and line segments to line segments. 2) Size transformations preserve orientation. 3) Size transformations preserve rations of distance. 4) Size transformations preserve angle measure. 5) Size transformations preserve perpendicularity 6) Size transformations take lines to parallel lines. Example 6 Find the image of parallelogram ABCD under the size transformation with center O and a scale factor of 3=k DC BAO Solution: A B' D'C' DC BAO
