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

Example 1:Horizontal Translation of R units:

H(x,y)=(x+h,y)OriginalA(-1,2)B(-1,-3)C(4,1)

(x+2, y)(1,2)(1,-3)(6,1)

Horizontal Translations move along the x-axis

Example 2:Vertical Translation of V units:

V(x,y)=(x,y+v)OriginalA(-1,2)B(-1,-3)C(4,1)

(x,y-3)(-1,-1)(-1,-6)(4,-2)

Vertical Translations move along the y-axis

Example 3:Horizontal & Vertical Translation of units:

(x,y)=(x+h,y+v)

OriginalA(-1,2)B(-1,-3)C(4,1)

(x-4,y+5)(-5,7)(-5,2)(0,6)

Example 4:Reflections Across the x-axis:

M(x,y)=(x,-y)

OriginalA(1,2)B(5,1)C(6,4)

(x,-y)(1,-2)(5,-1)(6,-4)

Example 5:Reflections Across the y-axis:

N(x,y)=(-x,y)

OriginalA(1,2)B(5,1)C(6,4)

(-x,y)(-1,2)(-5,1)(-6,4)

Example 6:180 degree rotation about the origin:

R(x,y)=(-x,-y)

OriginalA(2,5)B(4,1)C(6,7)

(-x,-y)(-2,-5)(-4,-1)(-6,-7)

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:

____________________

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:

____________________

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:

____________________

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:

____________________

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:

____________________

Describe the result of applying each rule to a figure in the coordinate plane.

F(x,y)=(x+7,y)

A(x,y)=(x-6,y+3)

C(x,y)=(x,y-5)

Z(x,y)=(-x,y)

T(x,y)=(x,-y)

W(x,y)=(-x,-y)

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:

____________________

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:

____________________

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:

____________________