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A dilation is not a basic rigid motion because it alters the size of a figure while maintaining its shape, rather than preserving distances between points. Rigid motions, such as translations, rotations, and reflections, only change the position or orientation of a figure without affecting its dimensions. In contrast, dilations involve scaling, which can either enlarge or reduce a figure, thus not satisfying the criteria of preserving lengths and angles.
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What is rigid motion?
Rigid motion refers to a transformation of a geometric figure that preserves distances and angles, meaning the shape and size of the figure remain unchanged. Common types of rigid motions include translations (sliding), rotations (turning), and reflections (flipping). In essence, during a rigid motion, the pre-image and its image are congruent. This concept is fundamental in geometry, as it helps in understanding symmetries and maintaining the integrity of shapes during transformations.
What is a rigid motion?
A rigid motion is a transformation in geometry that preserves the shape and size of a figure. This means that distances between points and angles remain unchanged during the transformation. Common types of rigid motions include translations, rotations, and reflections. Since the original figure and its transformed image are congruent, rigid motions do not alter the overall structure of the figure.
Why is translation a rigid motion?
Translation is considered a rigid motion because it involves moving every point of a shape or object the same distance in a specified direction, preserving its size and shape. During translation, there is no rotation or distortion; the relative distances and angles between points remain constant. This characteristic ensures that the object retains its original form and orientation throughout the motion.
Does an enlargement of a photograph represent a dilation or a rotation?
Dilation
What is rigid or semi-rigid?
Rigid is immovable, unbending. Semi-rigid can move in a limited way.
Is not a rigid motion transformation?
dilation (APEX)
What are not rigid motion transformations?
Dilation, shear, and rotation are not rigid motion transformations. Dilation involves changing the size of an object, shear involves stretching or skewing it, and rotation involves rotating it around a fixed point. Unlike rigid motions, these transformations may alter the shape or orientation of an object.
Which transformation is not a rigid transformation?
A rigid transformation means it has the same size and shape so it would be a dilation
What type of transformation is not considered rigid?
Flexing is one such transformation.
Does not describe a rigid motion transformation?
Stretch
What is rigid motion in geometry?
Movement of a shape can involve flexing - for example, a square frame being flexed into a rhombus. Rigid motion excludes such motion: the shape of the moving object does not change.
What doesn't describe a rigid motion transformation?
A rigid motion transformation is one that preserves distances and angles between points in a geometric shape. Anything that involves changing the size or shape of the object, such as scaling or shearing, would not describe a rigid motion transformation.
Difference between rigid body and particle?
The key difference between a particle and a rigid body is that a particle can undergo only translational motion whereas a rigid body can undergo both translational and rotational motion
What transformation preserves the shape and size?
Rigid motion
What are examples of rigid bodies that exhibit translational motion rotational motion and combination of both?
Planets
What has the author Edward Washington Suppiger written?
Edward Washington Suppiger has written: 'An analysis of the motion of a rigid body' -- subject(s): Dynamics, Rigid, Rigid Dynamics
What is the relationship between a translation and a rigid motion?
A translation is a type of rigid motion, which means it preserves distances and angles between points. In a translation, every point in a figure moves the same distance and direction. Rigid motions also include rotations and reflections.
