Which of the following is true for an isometry?
A.
The preimage is smaller than the image.
B.
The preimage is larger than the image.
C.
The preimage is the same size as the image.
D.
The preimage is in the same location as the image.
The correct answer is C. The preimage is the same size as the image.
An isometry is a transformation that preserves distance and shape. This means that the image created by an isometry is congruent (or identical) to the preimage. In other words, the preimage and the image have the same size and shape.
To understand this concept, let's consider a simple example. Suppose we have a square and we perform an isometry on it. The resulting image will also be a square, but it may be rotated, reflected, or translated in some way. However, it will have the same side lengths as the original square.
To determine the correct answer, we can eliminate the options that are not true for an isometry.
Option A states that the preimage is smaller than the image, which is incorrect. Isometries do not change the size of the object, so the preimage and image have the same size.
Option B states that the preimage is larger than the image, which is also incorrect. As mentioned before, isometries do not change the size of the object.
Option D states that the preimage is in the same location as the image. This is not always true for an isometry. While an isometry may preserve the relative positions of points, it can also move the object to a different location.
Therefore, the correct answer is C. The preimage is the same size as the image.