Warm-up ~ Hi! T(2, -3), A(-1, -2) and J(1, 2)

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Presentation transcript:

Warm-up ~ Hi! T(2, -3), A(-1, -2) and J(1, 2) 1. Reflect ΔTAJ over the x - axis. 2. Reflect ΔTAJ over y = x. 3. Reflect ΔTAJ over y = 1

Rotation A transformation in which a figure is turned about a fixed point, called the center of rotation. Center of Rotation

A Rotation is an Isometry Segment lengths are preserved. Angle measures are preserved. Parallel lines remain parallel. Orientation is unchanged.

Discovery Investigation!

90 counter-clockwise rotation Formula (x, y) _____________ A’(2, 4) A(4, -2)

Rotations are always counter-clockwise unless otherwise stated!!! 900: R90°(x, y) = (-y, x) 1800: R180°(x, y)= (-x, -y) 2700: R270°(x, y)= (y, -x) 90° rotation ( - , +) (-y, x) 0° rotation ( +, +) ( x, y) 180° rotation ( - , -) (- x - y) 270° rotation ( + , - ) ( y, - x)

Rotation Example Draw a coordinate grid and graph: A(-3, 0) B(-2, 4) Draw ABC A(-3, 0) C(1, -1) 9/21/2018

Rotation Example Rotate ABC 90 clockwise. Formula (x, y)  (y, x) 9/21/2018

Rotate ABC 90 clockwise. (x, y)  (y, x) A(-3, 0)  A’(0, 3) B(-2, 4)  B’(4, 2) C(1, -1)  C’(-1, -1) A’ B’ A(-3, 0) C’ C(1, -1) 9/21/2018

Rotate ABC 90 clockwise. Check by rotating ABC 90. A’ B’ A(-3, 0) C’ C(1, -1) 9/21/2018

Let’s Talk about Notation Again Rotations 900: R90°(x, y) = (-y, x) 1800: R180°(x, y)= (-x, -y) 2700: R270°(x, y)= (y, -x) Translation T(x, y) = (x + h, y + k) Line Reflections x-axis: y-axis: y=x: P(x, y) P’(x, -y) OR rx-axis(x, y) = (x, -y) P(x, y) P’(-x, y) OR ry-axis(x, y) = (-x, y) P(x, y) P’(-x, y) OR ry = x(x, y) = (y, x)

D(4, -3) R90° R180° rx-axis T(x+4, y-2) R270° ry-axis ry=x

G(-3, -4) R90° R180° rx-axis T(x+4, y-2) R270° ry-axis ry=x