Question

An isometry is a transformation that preserves _____.. A. direction. B. orientation. C. distance

Answer 1

The correct answer to this question is letter "C. distance." An isometry is a transformation that preserves distance. Isometry is a geometrical transformation that preserves geometrical properties such as distance. In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving injective map between metric spaces.

Answer 2

Answer: option C. distance.

Explanation:

1) You can use your etmyological knowledge, i.e. the origin of the words.

Iso means equal

metri means measurement

So, isometry meas equal measures, which is same distances.

2) Then, isometry are congruent transformations. They keep the distances, and, in consequence the angles of the figures.

Some transformations that are isometries are: translation, rotation and reflection.

When you translate a figure, all the parts are translated the same amount, and so the image is congruent to the preimage.

When you rotate a figure, also the distances of each point of the figure are preserved. The image and the preimaga are congruent.

The same happens with the reflections around a fixed axis or line.

On the other hand, dilations are not isometries, since the image will be enlarged or contracted as per the scale factor of the dilation.