Question

A composition of two isometries results in __________.

Answer 1

Definition: A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.

Four types of isometries:

1. Translation -- sliding a shape from one spot to another on the xy-plane;

2. Reflection -- creating a mirror image of a shape by reflecting a shape over a line, called the axis of reflection, on the xy-plane;

3. Rotation -- rotating a shape around a point, called the center of rotation, on the xy-plane;

4. Glide reflection -- a composite transformation which is a translation followed by a reflection in line parallel to the direction of translation.

Translations, reflections, and rotations don't change the shape or size of the shape being transformed, so we can see that these three types of transformations are isometric, the glide reflection doesn't change the shape or size of the shape being transformed, but changes orientation.

A composition or sequence of isometries occurs when two or more transformations are combined to form a new transformation. In a composition, one transformation produces an image upon which the other transformation is then performed (as for the glide reflection). The composition of isometries is always the isometry (preserves lengths).

Answer: correct choice is B.

Answer 2

A composition of two isometries results in preservation of length. The correct option among all the options that are given in the question is the second option or option "B". The other options can be easily negated. I hope that this is the answer that has actually come to your help.