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# Describing Reflections

Concept

## Reflection

A reflection is a transformation where each point in a figure is reflected, or mirrored, in a line. The line in which the points are reflected is known as the line of reflection.
A point, $P,$ in the preimage is reflected at a right angle in the line of reflection to a point, $P'.$ The points $P$ and $P'$ are the same distance away from the line of reflection.
Exercise

Reflect the triangle in the given line of reflection.

Solution

To reflect the given triangle, we can begin by marking the distance from the vertices to the line of reflection. The distances must intersect the line at right angles.

The vertices of the image lie the same distances away from, but on the other side of, the line of reflection.

Finally, we create the image by connecting the vertices with line segments.

info Show solution Show solution
Exercise

The quadrilateral $Q$ has been reflected to create $Q'.$ Sketch the line of reflection corresponding to the reflection.

Solution

By looking at the vertices, rather than the entire figures, it is possible to reliably find the line of reflection.

In a reflection, corresponding vertices are always the same distance away from the line of reflection. Thus, the line of reflection will lie half way between them. We can connect the corresponding vertices and mark the point halfway between them.

We can now draw the line of reflection.

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Concept

## Glide Reflection

A glide reflection is a transformation that combines a translation and a reflection. A line segment, $\overline{AB},$ transformed by a glide reflection might look like this. First it is translated to $\overline{A'B'}.$

Next it is reflected in the line of reflection to $\overline{A''B''}.$

A glide reflection could instead be a reflection followed by a translation, because the image created does not depend on the order of the transformations.

Concept

## Line Symmetry

A figure is said to have line symmetry if there exists a line such that, when the figure is reflected in the line it is mapped onto itself. In this case, the preimage and image are identical.

The line of reflection in which the figure has line symmetry is called line of symmetry. A figure can have more that one line of symmetry. For example, a square has four.