A transformation is rigid of which of the following occurs
A transformation is rigid if none of the following occurs:
- Translation: The objects do not move from their original positions.
- Rotation: The objects do not rotate or change their orientation.
- Scaling: The objects do not change size or shape.
- Shearing: The objects do not slant or skew.
A transformation is rigid if it preserves the shape and size of an object. In other words, a rigid transformation does not change the angles or lengths of the object's sides. The following transformations are considered rigid:
1. Translation: This is the movement of an object in a straight line without rotation or reflection. The shape and size of the object remain the same.
2. Rotation: This is the movement of an object around a fixed point by a certain angle. It preserves the shape and size of the object, while changing its orientation.
3. Reflection: This is the flipping of an object over a line, resulting in a mirror image. The shape and size of the object remain the same.
4. Glide Reflection: This is a combination of a translation and a reflection. It is a rigid transformation as it preserves the shape and size of the object.
Note that a dilation is not considered a rigid transformation because it changes the size of an object.
A transformation is rigid if and only if it preserves the distance between any two points. This means that if we have a pre-image and an image, the distance between corresponding points in the pre-image and image must remain the same after the transformation.
To determine if a transformation is rigid, we need to examine the transformation to see if it satisfies this property. Here are few examples of transformations that are rigid:
1. Translation: A translation is a transformation that moves every point in a figure or object the same distance and in the same direction. Since a translation preserves distances between points, it is considered a rigid transformation.
2. Rotation: A rotation is a transformation that turns a figure or object around a fixed point called the center of rotation. It preserves distances between points, as the points remain the same distance from the center of rotation, so it is considered a rigid transformation.
3. Reflection: A reflection is a transformation that flips a figure or object over a line, called the line of reflection. While a reflection changes the orientation of the figure, it does not affect distances between points, so it too is a rigid transformation.
On the other hand, non-rigid transformations do not preserve distances between points. For example:
1. Dilation: A dilation is a transformation that changes the size of a figure or object by a scale factor. Since distances between points are multiplied by the scale factor, a dilation is not considered a rigid transformation.
To determine if a transformation is rigid, we need to consider how the transformation affects distances between points.