9-2 Reflections

Reflection Across a Line

• Reflection across a line (called the line of reflection) is a transformation that produces an image with a opposite orientation from the preimage.–A reflection is an isometry.

Reflecting a Point Across a Line

• If point P(3, 4) is reflected across the line y = 1, what are the coordinates of its reflection image?

What is the image of the same point P reflected across the line x = -1?

Graphing a Reflection Image

• Graph points A(-3, 4), B(0, 1), and C(4, 2). What is the image of ΔABC reflected across the y-axis?

What is the image of ΔABC reflected across the x-axis?

9-3 Rotations

Rotation About a Point

• A rotation is a transformation that “turns” a figure around point R, called the center of rotation.– The positive number

of degrees a figure rotates is the angle of rotation.

– A rotation about a point is an isometry.

– Unless told otherwise, assume all rotations are counterclockwise.

Rotations of Regular Polygons

• The center of a regular polygon is the point that is equidistant from its vertices.

• The center and the vertices of a regular n-gon determine n congruent triangles.–Recall that the measure of each central

angle can be found by dividing 360 by n.• You can use this fact to find rotation images of

regular polygons.

Identifying a Rotation Image

• Point X is the center of regular pentagon PENTA. What is the image of each of the following:

– 72 rotation of T about X?

– 216 rotation of TN about X?

144 rotation of E about X?

Finding an Angle of Rotation

• Hubcaps of car wheels often have interesting designs that involve rotation. What is the angle of rotation about C that maps Q to X?

What is the angle of rotation about C that maps M to Q?

9-4 Symmetry

Types of Symmetry• A figure has symmetry if there is an isometry that maps the figure

onto itself.• A figure has line symmetry (also called

reflectional symmetry) if there is a reflection for which the figure is its own image.– The line of reflection is called a line of symmetry; it divides the

figure into congruent parts.• A figure has rotational symmetry if there is a

rotation of 180 or less for which the figure is its own image.– A figure with 180 rotational symmetry is also said to have point

symmetry because each segment joining a preimage with its image passes through the center of rotation.

Identifying Lines of Symmetry

• How many lines of symmetry does a regular hexagon have?

How many lines of symmetry does a rectangle have?

Identifying Rotational Symmetry

• Does the figure have rotational symmetry? If so, what is the angle of rotation?

Does the figure have rotational symmetry? If so, what is the angle of rotation?

• Does the figure have point symmetry?