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:
____________________