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Is reflecting a congruence transformation?
YES ---- Explanation: An isometry is a distance-preserving mapping. . Geometric figures which can be related by an isometry are called congruent. Reflection preserves distance so it is an isometry. It reverses orientation so it is called an indirect orientationl
Is reflection always an isometry?
No. While it is true for reflection in a straight line, it is not true for other reflections.
What is isometry that does not change orientation?
It's a transformation that's order of the letters like ABCD of a figure don't change when transformed.
Is line reflection a direct isometry?
if there is an even number of line reflections then yes. if there is n odd number of line reflections, then no.
Which properties are not preserved by an isometry?
An isometry preserves distances and angles between points, meaning that the shape and size of geometric figures remain unchanged. However, it does not necessarily preserve properties such as orientation (e.g., a reflection changes the orientation) or the position of points in space (e.g., a translation moves points). Additionally, while the overall configuration may remain intact, specific coordinates of points may change.
Is a rotation an isometry?
Yes, a rotation is an isometry.
Which type of isometry is the equivalent of two reflections across intersecting lines?
Rotation
What is theorem 5.12?
Theorem 5.12- A rotation is a composition of two reflections, and hence is an invertible isometry.
What point of transformation does not move in isometry?
In an isometry, the point of transformation that does not move is called the "fixed point." This point remains unchanged during the transformation, whether it is a translation, rotation, or reflection. For example, in a rotation, the center of rotation serves as the fixed point, while in a reflection, the line of reflection equidistantly bisects the space, with points on the line remaining unchanged.
Is a translation an Isometry?
Yes, translation is part of isometry.
What is an isometry?
A isometry is a transformation where distance (aka size) is preserved. In a dilation, the size is being altered, so no, it is not an isometry.
A preimage and an image are congruent in an isometry?
Yes. Being congruent is part of the definition of an isometry.
What is Isometry?
An isometry is a transformation in which the original figure and its image are congruent. Shape remains constant as size increases.
Explain why a glide reflection is an isometry?
Because the glide reflection is a combination of two isometries, it is also an isometry.
An isometry can be illustrated with a graphing calculator. Which function rule matches the isometry?
(x,y) (-x,-y)
Which transformation is not an isometry?
Dilation.
An isometry is a transformation that preserves?
no
