What is the composite of reflection?

Reflection A reflection is an example of a transformation that flips each point of a shape over the same line. Composite Transformation A composite transformation is when two or more transformations are combined to form a new image from the preimage.

Does order of reflections for a composition of two reflections in parallel lines matter?

Reflection over the Axes Theorem: If you compose two reflections over each axis, then the final image is a rotation of \begin{align*}180^\circ\end{align*} of the original. With this particular composition, order does not matter.

Are parallel lines reflections?

This demonstrates that two reflections over parallel line results the same as a single translation in a direction perpendicular to the parallel lines and with a magnitude twice the length of the distance between the parallel lines.

What does a composition of two isometries results in?

A composition of two isometries is an isometry. The composition of two reflections across two parallel lines is equivalent to a translation. The translation vector is perpendicular to the lines.

What are two reflections over parallel lines?

A composition of reflections over two parallel lines is equivalent to a translation. (May also be over any even number of parallel lines.) Example: Given a || b, and pre-image ΔABC, where parallel lines are vertical.

What is a composition of transformations?

A composition of transformations is a combination of two or more transformations, each performed on the previous image. A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines).

What is a composition of two transformations?

What is the composition of two reflections?

1. The composition of two reflections is a rotation.

What is a composition of Isometries?

– An isometry is uniquely determined by three non-collinear points and their images. – Any isometry is the composition of one, two or three reflections. – The composition of two reflections is either a translation or a rotation. – The composition of three reflections is either a reflection or a glide reflection.

What is the composition of two or more Isometries?

3. The composition of two isometries is an isometry.

What are the two reflections?

Two reflections over intersecting lines. Reflecting over two intersecting lines is the same as a rotation. Use this diagram to compare the angle of rotation with the angle of intersection of the lines of reflection. 1.

What is the result of compositions of reflections over parallel lines?

The compositions of reflections over parallel lines theorem states two things: If we perform a composition of two reflections over two parallel lines, the result is equivalent to a single translation transformation of the original object.

Which is the equivalent of a composition of reflections?

Parallel Lines Theorem A composition of reflections across two parallel lines is equivalent to a translation. (Or across any even number of parallel lines) A composition of reflections acrss three parallel lines is equivalent to a single reflection (or across any odd number of parallel lines) +

Is the composition of transformations and glide reflections the same?

A composition of reflections over intersecting lines is the same as a rotation (twice the measure of the angle formed by the lines). A glide reflection is a composition of transformations. In a glide reflection, a translation is first performed on the figure, then it is reflected over a line.

How to illustrate the composition of reflections theorem?

To illustrate the first part of this theorem, let’s perform a composition of reflections on a triangle over two parallel lines. In other words, let’s reflect the triangle over one of the lines and then reflect the resulting image over the other line.