![]() ![]() This year, we will always rotate about the origin. What is the line of reflection? How did the points change from the original to the reflection?ġ2 The concept of rotations can often be seen in wallpaper designs, fabrics, and art work.ġ3 This rotation is 90 degrees counterclockwise. Name the points of the reflected triangle. Name the points of the original triangle. If you folded the two shapes together line of reflection the two shapes would overlap exactly!ġ1 What happens to points in a Reflection? A reflection can be thought of as a "flipping" of an object over the line of reflection. ![]() The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection. In a mirror, for example, right and left are switched.ġ0 The line (where a mirror may be placed) is called the line of reflection. An object and its reflection have the same shape and size, but the figures face in opposite directions. We always go left or right first, then up or down.Ĩ A reflection can be seen in water, in a mirror, in glass, or in a shiny surface. The example shows how each vertex moves the same distance in the same direction.ħ In this example, the "slide" moves the figure 7 units to the left and 3 units down. ![]() Each coordinate point follows the same rule. The movement of each coordinate point is actually a function. Translations are SLIDESĦ Let's examine some translations related to coordinate geometry. This is referred to as the same orientation. The original object and its translation have the same shape and size, and they face in the same direction. It is common practice to name shapes using capital letters: The original figure is called the pre-image It is common practice to name transformed shapes using the same letters with a “prime” symbol: The transformed figure is called the image.Ī translation "slides" an object a fixed distance in a given direction. The transformations you will learn about include: Translation Rotation Reflection In geometry, there are specific ways to describe how a figure is changed. According to Chasles' theorem, every rigid transformation can be expressed as a screw displacement.Presentation on theme: "1.3 RIGID MOTIONS."- Presentation transcript:Įssential Question: What properties of a figure are preserved under a translation, reflection, or rotation? September 9, 2014 In kinematics, proper rigid transformations in a 3-dimensional Euclidean space, denoted SE(3), are used to represent the linear and angular displacement of rigid bodies. The set of proper rigid transformations is called special Euclidean group, denoted SE( n). The set of all (proper and improper) rigid transformations is a mathematical group called the Euclidean group, denoted E( n) for n-dimensional Euclidean spaces. Any proper rigid transformation can be decomposed into a rotation followed by a translation, while any improper rigid transformation can be decomposed into an improper rotation followed by a translation, or into a sequence of reflections.Īny object will keep the same shape and size after a proper rigid transformation.Īll rigid transformations are examples of affine transformations. (A reflection would not preserve handedness for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a proper rigid transformation, or rototranslation. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. The rigid transformations include rotations, translations, reflections, or any sequence of these. ![]() In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points. ![]()
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