![]() A line through O is transformed onto itself, and line not through O is transformed into a parallel line.Ĭ. A segment AB not belonging to the line through the center O is transformed on to the segment A'B' parallel to ABī. A dilation is a similarity transformation.Ī. When k < 0, P is mapped to P' on the opposite side of point O such that OP' = |k|OP.ġ. Why do you suppose the scale factor was defined to be a positive number? Note that we are dealing with distance.įor a dilation (or homothety or homothecy) the transformation is usually defined for k < 0 as well. O is called the center of similitude or the center of dilation. ![]() If 0 0, assigns to each point P a point P' such that OP' = kOP (Note typo in book where this is given as OP' = kOA). If k = 1, the transformation is an isometry. Is called a scale factor, or similarity ratio, or similarity coefficient, or. No similarity transformation exists because the circled corresponding distances and the corresponding distances marked by the arrows on Figure B are not in the same ratio.Overview of Section 5.4 Similarity transformations and constructionsĪ transformation S k of the plane that multiplies all distances by the same positive constant k is a similarity of the plane. Is there a sequence of dilations and basic rigid motions that takes the small figure to the large figure? Take measurements as needed. One possible solution: We first take a dilation of Figure A with a scale factor of r < 1 and center O, the point where the two line segments meet, until the corresponding lengths are equal to those in Figure A Next, take a rotation (180°) about O, and then, finally, take a reflection over a (vertical) line t. Which transformations compose the similarity transformation that maps Figure A onto Figure A’? Eureka Math Geometry Module 2 Lesson 12 Exit Ticket Answer Keyįigure A’ is similar to Figure A. To be a dilation of the plane, a constant scale factor must be used for all points from the center of dilation however, the scale factor relating the distances from the center in the diagram range from 2 to 2.5. ![]() The diagram does not show a dilation of the plane from point O, even though the corresponding points are collinear with the center O. The diagram below shows a dilation of the plane … or does it? Explain your answer. Is there a sequence of dilations and basic rigid motions that takes the large figure to the small figure? Take measurements as needed.Ī similarity transformation that maps segment AB to segment WX would need to have scale factor of about \(\frac\). Finally, translate Figure 1 by a vector so that Figure 1 coincides with Figure 2. Then, reflect Figure 1 over a vertical line t. The solution image reflects this approach, but students may say to first rotate Figure 1 around a center C by 90° in the clockwise direction. However, to do this, the correct center must be found. It is possible to only use two transformations: a rotation followed by a reflection. Which transformations compose the similarity transformation that maps Figure 1 onto Figure 2? Then, S must be rotated around a center C of degree θ so that S coincides with S’.įigure 1 is similar to Figure 2. Which transformations compose the similarity transformation that maps S onto S’?įirst, dilate S by a scale factor of r > 1 until the corresponding segment lengths are equal in measurement to those of S’. → Step 1: The dilation has a scale factor of r 1 until the corresponding lengths are equal in measurement, and then reflect over a line iso that Figure 1 coincides with Figure 2.įigure S is similar to Figure S’. → We are not looking for specific parameters (e.g., scale factor or degree of rotation of each transformation) rather, we want to identify the series of transformations needed to map Figure Z to Figure Z’. ![]() Describe a transformation that maps Figure Z onto Figure z’. Engage NY Eureka Math Geometry Module 2 Lesson 12 Answer Key Eureka Math Geometry Module 2 Lesson 12 Example Answer Keyįigure Z’ is similar to Figure Z. ![]()
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