Which of the following is true for an isometry?
(1 point)
Responses
The preimage and the image are congruent.
The preimage and the image are congruent.
The preimage is larger than the image.
The preimage is larger than the image.
The preimage is smaller than the image.
The preimage is smaller than the image.
The preimage is the same position as the image.
The correct answer is: The preimage and the image are congruent.
The correct answer is: "The preimage and the image are congruent."
To understand why this is true for an isometry, we need to define what an isometry is. An isometry is a transformation in geometry that preserves distance, angle measures, and shape. In other words, when you apply an isometry to a figure (preimage), the resulting figure (image) is congruent to the original figure.
To determine if the preimage and image are congruent for a given transformation, you need to follow these steps:
1. Identify the type of transformation: Isometry transformations include translations, rotations, reflections, and combinations of these.
2. Apply the transformation to the preimage: Perform the specified transformation on the preimage to obtain the image. For example, if the transformation is a translation, you would shift the preimage by a certain distance and direction to create the image.
3. Compare the preimage and the image: Check if the preimage and image have the same shape and corresponding sides and angles of equal measures. If they do, they are congruent.
In the case of an isometry, regardless of the type of transformation applied, the resulting image will always be congruent to the preimage. This is because isometries preserve all the geometric properties that define congruence, such as side lengths, angle measures, and shape. Therefore, the correct response is that the preimage and the image are congruent.