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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.

Reflect the triangle in the given line of reflection.

Show 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.

The quadrilateral Q has been reflected to create $Q_{′}.$ Sketch the line of reflection corresponding to the reflection.

Show 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.

Next it is reflected in the line of reflection to $A_{′′}B_{′′}.$

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.

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.

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