9.3 – Perform Reflections.

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Presentation transcript:

9.3 – Perform Reflections

Reflection: Transformation that uses a line like a mirror to reflect an image Line of Reflection: Mirror line in a reflection

A reflection in a line m maps every point P in the plane to a point , such that: If P is not on m, then m is the perpendicular bisector of If P is on m, then

Reflect point P(5, 7) in the given line. x – axis P(5, 7) becomes P A reflection in the x-axis changes (x, y) into _______ (x, –y)

Reflect point P(5, 7) in the given line. y – axis P(5, 7) becomes P A reflection in the y-axis changes (x, y) into _______ (–x, y)

Reflect point P(5, 7) in the given line. y = x P(5, 7) becomes P A reflection in the y = x changes (x, y) into _______ (y, x)

Graph the reflection of the polygon in the given line. x – axis

Graph the reflection of the polygon in the given line. y – axis

y = x (–1 , –3) (–3, –1) (2, –4 ) (–4, 2) (3, 0) (0, 3) Graph the reflection of the polygon in the given line. y = x (–1 , –3) (–3, –1) (2, –4 ) (–4, 2) (3, 0) (0, 3)

Graph the reflection of the polygon in the given line. x – axis

Graph the reflection of the polygon in the given line. x = –1

Graph the reflection of the polygon in the given line.

9.4 – Perform Rotations

Rotation: Transformation that turns a figure about a fixed point Center of Rotation: The point that the rotation happens around Angle of Rotation: Degree the figure is rotated counterclockwise

A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that: If Q is not the center of rotation, then and x° Q P

A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that: If Q is the center of rotation, then Q

1. Match the diagram with the angle of rotation. B. 90°

1. Match the diagram with the angle of rotation.

1. Match the diagram with the angle of rotation.

Counter-clockwise degree of rotation: _______ 180° State if the rotation is 90°, 180°, or 270° counter-clockwise. Counter-clockwise degree of rotation: _______ 180°

Counter-clockwise degree of rotation: _______ 90° State if the rotation is 90°, 180°, or 270° counter-clockwise. Counter-clockwise degree of rotation: _______ 90°

Counter-clockwise degree of rotation: _______ 270° State if the rotation is 90°, 180°, or 270° counter-clockwise. Counter-clockwise degree of rotation: _______ 270°

6. Find the value of each variable in the rotation. x = 4 z = 3 y = z + 2 y = 3 + 2 y = 5

6. Find the value of each variable in the rotation. 4s = 24 s = 6 r = 2s – 3 r = 2(6) – 3 r = 12 – 3 r = 9

HW Problems 9.3 9.4 593-594 602-605 WS 3-7, 9, 12 (Graph on worksheet) 3-8, 20, 21, 44-46 ROTATION WS 9.3 #7