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What are the properties of reflections and rotations and translations?
the image that is reflected is counterclockwise to the original
What are the three types of congruence transformations?
The three types of congruence transformations are translations, rotations, and reflections. Translations slide a figure from one location to another without changing its shape or orientation. Rotations turn a figure around a fixed point, maintaining its size and shape. Reflections flip a figure over a line, creating a mirror image while preserving distances and angles.
When the preimage and image are congruent the transformation is called an isometry true or false?
True. An isometry is a transformation that preserves distances and angles, meaning that the preimage and image are congruent. Examples of isometries include translations, rotations, and reflections, all of which maintain the shape and size of geometric figures.
Which transformation does not produce a congruent image?
A transformation that does not produce a congruent image is a dilation. While dilations change the size of a figure, they maintain the shape, meaning the resulting image is similar but not congruent to the original. In contrast, transformations such as translations, rotations, and reflections preserve both size and shape, resulting in congruent images.
What term describes a transformation that does not change a figure's size or shape?
The term that describes a transformation that does not change a figure's size or shape is "isometry." Isometric transformations include translations, rotations, and reflections, which maintain the original dimensions and angles of the figure. As a result, the pre-image and image of the transformation are congruent.
What are the properties of reflections and rotations and translations?
the image that is reflected is counterclockwise to the original
Identify the transformation(s) where the image has the same orientation as the preimage.?
Transformations that preserve the orientation of the image relative to the preimage include translations, rotations, and dilations. These transformations maintain the order of points and the overall direction of the figure. In contrast, reflections and certain types of glide reflections change the orientation, resulting in a mirror image. Therefore, only translations, rotations, and dilations keep the same orientation as the original figure.
When the preimage and image are congruent the transformation is called an isometry true or false?
True. An isometry is a transformation that preserves distances and angles, meaning that the preimage and image are congruent. Examples of isometries include translations, rotations, and reflections, all of which maintain the shape and size of geometric figures.
Which transformation does not produce a congruent image?
A transformation that does not produce a congruent image is a dilation. While dilations change the size of a figure, they maintain the shape, meaning the resulting image is similar but not congruent to the original. In contrast, transformations such as translations, rotations, and reflections preserve both size and shape, resulting in congruent images.
What three transformations have isometry?
The three transformations that have isometry are translations, rotations, and reflections. Each of these transformations preserves the distances between points, meaning the shape and size of the figure remain unchanged. As a result, the original figure and its image after the transformation are congruent.
What term describes a transformation that does not change a figure's size or shape?
The term that describes a transformation that does not change a figure's size or shape is "isometry." Isometric transformations include translations, rotations, and reflections, which maintain the original dimensions and angles of the figure. As a result, the pre-image and image of the transformation are congruent.
What transformation is not a congruent image?
A transformation that is not a congruent image is a dilation. Unlike rigid transformations such as translations, rotations, and reflections that preserve shape and size, dilation changes the size of a figure while maintaining its shape. This means that the original figure and the dilated figure are similar, but not congruent, as their dimensions differ.
Which transformation does not always result in an image that is congruent to the original figure?
A dilation (or scaling) is a transformation that does not always result in an image that is congruent to the original figure. While translations, rotations, and reflections always produce congruent figures, dilations change the size of the figure, which means the image may be similar to, but not congruent with, the original figure.
How are coordinates of the image related to the coordinates of the preimage?
The coordinates of the image are typically related to the coordinates of the preimage through a specific transformation, which can include translations, rotations, reflections, or dilations. For example, if a transformation is defined by a function or a matrix, the coordinates of the image can be calculated by applying that function or matrix to the coordinates of the preimage. Thus, the relationship depends on the nature of the transformation applied.
What is the transformation in which the preimage and it image are congruent?
The transformation in which the preimage and its image are congruent is called a rigid transformation or isometry. This type of transformation preserves distances and angles, meaning that the shape and size of the figure remain unchanged. Common examples include translations, rotations, and reflections. As a result, the original figure and its transformed version are congruent.
Can the isometric transformation change size?
No, isometric transformations do not change the size of shapes. They preserve distances and angles, meaning that the original shape and its image after the transformation will have the same dimensions. Examples of isometric transformations include translations, rotations, and reflections, which maintain the object's size and shape.
What describes a rigid motion transformation?
A rigid motion transformation is a type of transformation that preserves the shape and size of geometric figures. This means that distances between points and angles remain unchanged during the transformation. Common examples include translations, rotations, and reflections. Essentially, a rigid motion maintains the congruence of the original figure with its image after the transformation.
