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May 4, 2022 · There are four kinds of rigid motions: translations, rotations, reflections, and glide-reflections. When describing a rigid motion, we will use points like P and Q, located on the geometric shape, and identify their new location on the moved geometric shape by P' and Q'.
- Reflection as Rigid Transformation
- Translation as Rigid Transformation
- Rotation as Rigid Transformation
- Solution
- Example 2
- Practice Question
In reflection, the position of the points or object changes with reference to the line of reflection. When learning about point and trianglereflection, it has been established that when reflecting a pre-image, the resulting image changes position but retains its shape and size. This makes reflection a rigid transformation. The graph above showcases...
Translation is also a rigid transformation because itsimply “moves” the pre-image on a position to construct the final image of the transformation. When translating an object, it is possible to move along the horizontal direction, vertical direction, or even both. Take a look at the translation performed on the triangle ΔABC. The triangle ΔABC is t...
In rotation, the pre-image is “turned” for a given angle in either a clockwise or counter-clockwise directionand with respect to a given point. This makes it a rigid transformation because the resulting image retains the size and shape of the pre-images. Here’s an example of a rotation involving ΔABC, where it is turned at an angle of 90∘in a count...
Observe each pair of pre-image and images then try to describe the transformations appliedon each of the objects. 1. The size and shape of both A and A′ are identical. The only difference is that A′ is the result of translating Ato the right and downward. 2. Now, focus on B and B′. The image of B is the result of rotating it 90∘to the counter-clock...
The triangle ΔABCis graphed on the rectangular coordinate system. The vertices of the triangle have the following coordinates: A=(2,2)B=(8,4)C=(4,10) If ΔABC is translated 10 units to the left and 2 units upward, what are the coordinates of ΔA′B′C′? Use the resulting image to confirm that the transformations applied were all rigid.
1. Which of the following transformations do not exhibit rigid transformation? A. B→B′ B. B→D′ C. B→B′ and C→C′ D. A→A′ and D→D′ 2. The triangle, ΔABC, is graphed on the rectangular coordinate system. The vertices of the triangle have the following coordinates: A=(8,2)B=(14,2)C=(14,8) If ΔABC is translated over the line of reflection y=x and transl...
A rigid motion of a object is the act of moving he object to a position without changing the object’s shape or size. The object P is moved, but its shape and size are not changed. These are not rigid motions. rigid motion followed by a rigid motion is again a rigid motion.
Rigid motions are also called congruence transformations because the preimage and its image under a rigid motion are congruent figures. Some examples of rigid motions are translations, reflections, and rotations.
A rigid motion is a transformation (of the plane) that "preserves distance". In other words, if A is sent/mapped/transformed to A′ and B is sent to B′, then the distance between A and B (the length of segment AB) is the same as the distance between A′ and B′ (the length of segment A′B′).
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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Examples of rigid motions include translations, rotations, and reflections. In the context of the coordinate plane, transformations can be visualized as mappings from one set of points to another. For instance, reflecting a shape across a vertical line will only change the x-coordinates of its points.
