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?