PPT-Geometry Transformation Dilation

8 th Math Presented by Mr Laws Standard 8G3 Describe the effect of dilations translations rotations and reflections on twodimensional figures using coordinates Essential Question. Objective: . Dilation. What is a . Dilation. ?. A dilation is a transformation that changes the size but not the shape of the figure. . We use “ .  ” to identify new points. . A Dilation can enlarge or reduce a figure by a . Unit 4.04. Vocabulary. Dilation: . A transformation . in which a figure is made larger or smaller with respect to a point called the center of dilation.. Example: . The . red. polygon has been . Dilated. Color . Camera models, camera calibration. Advanced image pre-processing . Line detection. Corner detection. Maximally stable extremal regions. Mathematical Morphology. . binary. gray-scale. skeletonization. Dilation. A . transformation in which a figure is enlarged or reduced with respect to a fixed point . C. called the center of dilation and a scale factor . k, . which is the ratio of lengths of the corresponding sides of the image and . Color . Camera models, camera calibration. Advanced image pre-processing . Line detection. Corner detection. Maximally stable extremal regions. Mathematical Morphology. . binary. gray-scale. skeletonization.   WARM-UP . STRETCH. Today you will investigate a transformation called a . dilation.  that enlarges or reduces a figure while maintaining its shape.  After creating new enlarged polygons, you and your team will explore the relationships that exist among polygons that look alike but are different sizes. Given: ∠ACB . ∠. EDB and . Prove: . Δ. ABC . . Δ. EBD.  . Given: ∠ACB . ∠. EDB and . Prove: . Δ. AFD. . Δ. EFC.  . F. Dilation. A dilation is a transformation that enlarges or reduces an image proportionally. The corresponding angles are congruent, but the corresponding sides are proportional. . Distributive property . and . Similarity. Vocabulary. Dilation: Increases or decreases the size of an object by a scale factor ( r ), with out changing the shape of the object. . Scale Factor: Ratio of the pre-image to the image; the factor that is used to increase or decrease the size of an object. . By Brit Caswell. What is a Dilation?. Pg. 587. A stretch! . Think of Ant Man!. Is a dilation a rigid motion?. If the scale factor is . <. 1. , the dilation is called a . reduction. .. If the scale factor is . dilation. .. Enlarging or reducing a figure is called dilation.. A . dilated . figure is similar to its original figure. What two things must be true for figures to be similar.. 1.. 2.. The . ratio. p. 511. You identified congruence transformations.. Identify similarity transformations.. Verify similarity after a similarity transformation.. Definitions. Transformation. – an operation that maps an original figure (. Draw dilations.. Draw dilations in the coordinate plane.. Definitions. A . dilation. or scaling is a similarity transformation that enlarges or reduces a figure proportionally with respect to a center point and a scale factor.. Geometry in Nature is Everywhere. Proportions of the human body. In the shape of a shell. .. .. . .. . The bees make their hives into regular hexagons. Honeycomb. The following slides are some more examples of geometry in nature. Mass and Energy.. Relativistic length contraction using the Lorentz transformation. .. Time dilation using the inverse Lorentz transformation.. for B.Sc.(H)Physics, Part-1, Paper-I, Group-A. By. SHASHI KANT KUMAR.