Warm Up. 9.2 Reflections Using Reflections in a Plane One type of transformation uses a line that acts like a mirror, with an image reflected in the.

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Presentation transcript:

Warm Up

9.2 Reflections

Using Reflections in a Plane One type of transformation uses a line that acts like a mirror, with an image reflected in the line. This transformation is a reflection and the mirror line is the line of reflection.

Using Reflections in a Plane A reflection in a line m is a transformation that maps every point P in the plane to a point P′, so that the following properties are true: 1.If P is not on m, then m is the perpendicular bisector of PP′.

Using Reflections in a Plane A reflection in a line m is a transformation that maps every point P in the plane to a point P′, so that the following properties are true: 2.If P is on m, then P = P′

Example 1: Reflections in a Coordinate Plane Graph the given reflection. a.H (2, 2) in the x-axis b.G (5, 4) in the line y = 4

Example 1: Reflections in a Coordinate Plane Graph the given reflection. a.H (2, 2) in the x-axis Solution: Since H is 2 units above the x-axis, its reflection, H′, is two units below the x-axis

Example 1: Reflections in a Coordinate Plane Graph the given reflection. b.G (5, 4) in the line y = 4 Solution. Start by graphing y = 4 and G. From the graph, you can see that G is on the line. This implies G = G′

Properties of Reflections Reflections in the coordinate axes have the following properties: 1.If (x, y) is reflected in the x-axis, its image is the point (x, -y). 2.If (x, y) is reflected in the y-axis, its image is the point (-x, y).