![]() ![]() The rigid transformations include rotations, translations, reflections, or any sequence of these. Is the image of a rigid transformation is congruent to its preimage? WHY OR WHY NOT? Convince your partner.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. The dictionary definition of rigid is: not bending or easily moved into a different shape Why do you think that these three transformations are considered rigid?ġ9 Rigid Transformation A movement that preserves Angle measure Distance between points Parallel lines A transformation is said to be moved or mapped from the preimage to its image.Ģ0 Turn and Talk: ONE MINUTE FOR EACH PARTNER. Has each picture been rotated in a clockwise or counter-clockwise direction? The birds were rotated clockwise and the fish counterclockwise.ġ8 Translations, Reflections, and Rotations are considered Rigid Transformations. Using your whiteboards: Does this picture show a translation, rotation, or reflection? How do you know? Rotationġ6 Does this picture show a translation, rotation, or reflection?ġ7 The birds were rotated clockwise and the fish counterclockwise. An object and its rotation are the same shape and size, but the figures may be turned in different directions.ġ5 Does this picture show a translation, rotation, or reflection? Clockwise Counterclockwiseġ4 A rotation is a transformation that turns a figure about a fixed point called the center of rotation. 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. 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 ![]()
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