Answered

What is the difference between an
isometric transformation and one that is not isometric? Give examples of least
two isometric transformations and at least one non-isometric
transformation.

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Isometric transformations are transformations of the objects' position without diminishing the image or object, retaining its original shape. Furthermore, isometric transformations have three types of examples, namely, translation, reflection and rotation. These examples only alter the image either by sliding up or down, sideways or diagonally (translation), symmetry or mirror image (reflection) or clockwise and counter-clockwise in angle (rotation). While non-isometric transformations are transformations that modify, change and alter the dimension or shape of the object. An example is enlargement, in which this increases or decreases the size of the image or object.



The correct answer is:

An isometric transformation is one in which the shape and size of the figure does not change. A non-isometric transformation is one in which the figure changes size or shape.

Explanation:

An isometry is defined as a transformation that maintains congruence; this means the image is the same shape and size as the pre-image. It also means that if a transformation is not an isometry, then congruence is not maintained.

Reflections, rotations, and translations are all examples of isometries. Reflections give us a mirror image of the figure; rotations turn the figure; and translations slide the figure.

Dilations are examples of transformations that are not isometries. A dilation stretches or shrinks the image, so it changes the size.

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