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1.7 Motion in the Coordinate Plane

1.7 Motion in the Coordinate Plane. Objectives: -Review algebraic concepts including the coordinate plane, origin, x- and y- coordinates, and ordered pair. -Construct translations, reflections across axes, and rotations about the origin of the coordinate plane. Warm-Up:

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1.7 Motion in the Coordinate Plane

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  1. 1.7 Motion in the Coordinate Plane Objectives: -Review algebraic concepts including the coordinate plane, origin, x- and y- coordinates, and ordered pair. -Construct translations, reflections across axes, and rotations about the origin of the coordinate plane. Warm-Up: Graph the following points. A(2,5), B(-3,6), C(-4,-1), D(5,-7) Label the x- & y axes, origin, & quadrants 1,2,3,&4

  2. Example 1: Horizontal Translation of R units: H(x,y)=(x+h,y) Original A(-1,2) B(-1,-3) C(4,1) (x+2, y) (1,2) (1,-3) (6,1) Horizontal Translations move along the x-axis

  3. Example 2: Vertical Translation of V units: V(x,y)=(x,y+v) (x,y-3) (-1,-1) (-1,-6) (4,-2) Original A(-1,2) B(-1,-3) C(4,1) Vertical Translations move along the y-axis

  4. Example 3: Horizontal & Vertical Translation of units: (x,y)=(x+h,y+v) (x-4,y+5) (-5,7) (-5,2) (0,6) Original A(-1,2) B(-1,-3) C(4,1)

  5. Example 4: Reflections Across the x-axis: M(x,y)=(x,-y) Original A(1,2) B(5,1) C(6,4) (x,-y) (1,-2) (5,-1) (6,-4)

  6. Example 5: Reflections Across the y-axis: N(x,y)=(-x,y) Original A(1,2) B(5,1) C(6,4) (-x,y) (-1,2) (-5,1) (-6,4)

  7. Example 6: 180 degree rotation about the origin: R(x,y)=(-x,-y) Original A(2,5) B(4,1) C(6,7) (-x,-y) (-2,-5) (-4,-1) (-6,-7)

  8. Use the given rule to transform the figure. Label the coordinates of the preimage & image. (x,y)=(x+4,y) ∆ABC∆A1B1C1 A :______ A1 :______ B : ______ B1 : ______ C : ______ C1 : ______ Type of transformation: ____________________

  9. Use the given rule to transform the figure. Label the coordinates of the preimage & image. (x,y)=(x+6,y-2) ∆PQR∆P1Q1R1 P :______ P1 :______ Q : ______ Q1 : ______ R : ______ R1 : ______ Type of transformation: ____________________

  10. Use the given rule to transform the figure. Label the coordinates of the preimage & image. (x,y)=(x,-y) ∆LMN∆L1M1N1 L :______ L1 :______ M : ______ M1 : ______ N : ______ N1 : ______ Type of transformation: ____________________

  11. Use the given rule to transform the figure. Label the coordinates of the preimage & image. (x,y)=(-x, y) ∆LMN∆L1M1N1 L :______ L1 :______ M : ______ M1 : ______ N : ______ N1 : ______ Type of transformation: ____________________

  12. Use the given rule to transform the figure. Label the coordinates of the preimage & image. (x,y)=(-x,-y) ∆LMN∆L1M1N1 L :______ L1 :______ M : ______ M1 : ______ N : ______ N1 : ______ Type of transformation: ____________________

  13. Describe the result of applying each rule to a figure in the coordinate plane. F(x,y)=(x+7,y) Z(x,y)=(-x,y) A(x,y)=(x-6,y+3) T(x,y)=(x,-y) C(x,y)=(x,y-5) W(x,y)=(-x,-y)

  14. Write the rule in the form T(x,y)=(?,?) that describes the transformation pictured. (x,y)=( ___ , ___ ) ∆ABC∆A1B1C1 A :______ A1 :______ B : ______ B1 : ______ C : ______ C1 : ______ Type of transformation: ____________________

  15. Write the rule in the form T(x,y)=(?,?) that describes the transformation pictured. (x,y)=( ___ , ___ ) ∆PQR∆P1Q1R1 P :______ P1 :______ Q : ______ Q1 : ______ R : ______ R1 : ______ Type of transformation: ____________________

  16. Write the rule in the form T(x,y)=(?,?) that describes the transformation pictured. (x,y)=( ___ , ___ ) ∆LMN∆L1M1N1 L :______ L1:______ M : ______ M1: ______ N : ______ N1: ______ Type of transformation: ____________________

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