# 12.7: Chapter 12 Review

Difficulty Level:

**At Grade**Created by: CK-12Turn In

**Keywords & Theorems**

- Line of Symmetry
- A line that passes through a figure such that it splits the figure into two congruent halves.

- Line Symmetry
- When a figure has one or more lines of symmetry.

- Rotational Symmetry
- When a figure can be rotated (less that \begin{align*}360^\circ\end{align*}) and it looks the same way it did before the rotation.

- Center of Rotation
- The point at which the figure is rotated around such that the rotational symmetry holds. Typically, the center of rotation is the center of the figure.

- angle of rotation
- The angle of rotation, tells us how many degrees we can rotate a figure so that it still looks the same.

- Transformation
- An operation that moves, flips, or changes a figure to create a new figure.

- Rigid Transformation
- A transformation that preserves size and shape.

- Translation
- A transformation that moves every point in a figure the same distance in the same direction.

- Vector
- A quantity that has direction and size.

- Reflection
- A transformation that turns a figure into its mirror image by flipping it over a line.

- Line of Reflection
- The line that a figure is reflected over.

- Reflection over the \begin{align*}y-\end{align*}axis
- If \begin{align*}(x,y)\end{align*} is reflected over the \begin{align*}y-\end{align*}axis, then the image is \begin{align*}(-x,y)\end{align*}.

- Reflection over the \begin{align*}x-\end{align*}axis
- If \begin{align*}(x,y)\end{align*} is reflected over the \begin{align*}x-\end{align*}axis, then the image is \begin{align*}(x,-y)\end{align*}.

- Reflection over \begin{align*}x = a\end{align*}
- If \begin{align*}(x, y)\end{align*} is reflected over the vertical line \begin{align*}x = a\end{align*}, then the image is \begin{align*}(2a - x, y)\end{align*}.

- Reflection over \begin{align*}y = b\end{align*}
- If \begin{align*}(x, y)\end{align*} is reflected over the horizontal line \begin{align*}y = b\end{align*}, then the image is \begin{align*}(x, 2b - y)\end{align*}.

- Reflection over \begin{align*}y = x\end{align*}
- If \begin{align*}(x, y)\end{align*} is reflected over the line \begin{align*}y = x\end{align*}, then the image is \begin{align*}(y, x)\end{align*}.

- Reflection over \begin{align*}y = -x\end{align*}
- If \begin{align*}(x, y)\end{align*} is reflected over the line \begin{align*}y = -x\end{align*}, then the image is \begin{align*}(-y, -x)\end{align*}.

- Rotation
- A transformation by which a figure is turned around a fixed point to create an image.

- Center of Rotation
- The fixed point that a figure is rotated around.

- Rotation of \begin{align*}180^\circ\end{align*}
- If \begin{align*}(x, y)\end{align*} is rotated \begin{align*}180^\circ\end{align*} around the origin, then the image will be \begin{align*}(-x, -y)\end{align*}.

- Rotation of \begin{align*}90^\circ\end{align*}
- If \begin{align*}(x, y)\end{align*} is rotated \begin{align*}90^\circ\end{align*} around the origin, then the image will be \begin{align*}(-y, x)\end{align*}.

- Rotation of \begin{align*}270^\circ\end{align*}
- If \begin{align*}(x, y)\end{align*} is rotated \begin{align*}270^\circ\end{align*} around the origin, then the image will be \begin{align*}(y, -x)\end{align*}.

- Composition (of transformations)
- To perform more than one rigid transformation on a figure.

- Glide Reflection
- A composition of a reflection and a translation. The translation is in a direction parallel to the line of reflection.

- Reflections over Parallel Lines Theorem
- If you compose two reflections over parallel lines that are \begin{align*}h\end{align*} units apart, it is the same as a single translation of \begin{align*}2h\end{align*} units.

- 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.

- Reflection over Intersecting Lines Theorem
- If you compose two reflections over lines that intersect at \begin{align*}x^\circ\end{align*}, then the resulting image is a rotation of \begin{align*}2x^\circ\end{align*}, where the center of rotation is the point of intersection.

- Tessellation
- A tiling over a plane with one or more figures such that the figures fill the plane with no overlaps and no gaps.

## Review Questions

Match the description with its rule.

- Reflection over the \begin{align*}y-\end{align*}axis - A. \begin{align*}(2a - x, y)\end{align*}
- Reflection over the \begin{align*}x-\end{align*}axis - B. \begin{align*}(-y, -x)\end{align*}
- Reflection over \begin{align*}x = a\end{align*} - C. \begin{align*}(-x, y)\end{align*}
- Reflection over \begin{align*}y = b\end{align*} - D. \begin{align*}(-y, x)\end{align*}
- Reflection over \begin{align*}y = x\end{align*} - E. \begin{align*}(x, -y)\end{align*}
- Reflection over \begin{align*}y = -x\end{align*} - F. \begin{align*}(x, 2b - y)\end{align*}
- Rotation of \begin{align*}180^\circ\end{align*} - G. \begin{align*}(x, y)\end{align*}
- Rotation of \begin{align*}90^\circ\end{align*} - H. \begin{align*}(-x, -y)\end{align*}
- Rotation of \begin{align*}270^\circ\end{align*} - I. \begin{align*}(y, -x)\end{align*}
- Rotation of \begin{align*}360^\circ\end{align*} - J. \begin{align*}(y, x)\end{align*}

## Texas Instruments Resources

*In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9697.*

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Date Created:

Feb 22, 2012
Last Modified:

Aug 15, 2016
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