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?