Rotations, Dilations, and Sequences of Transformations

Give the coordinates of the image.

Rhombus ABCD with vertices A(2,6), B(6,7), C(5,3), and D(1,2) :

Rotation of 180 degrees about the origin

• A'(-2,-6)

  B'(-6,-7)

  C'(-5,-3)

  D'(-1,-2)

• A'(2,6)

  B'(6,7)

  C'(5,3)

  D'(1,2)

• A'(-4,-5)

  B'(-2,0)

  C'(-1,-3)

  D'(-1,-7)

Give the coordinates of the image.

Trapezoid STUV with vertices S(-7,-1), T(-2,-3), U(-2,-5), and V(-7,7) :

Rotation of 90 degrees counterclockwise about the origin

• S'(1,-7)

  T'(3,-2)

  U'(5,-2)

  V'(7,-7)

• S'(-1,-7)

  T'(-3,-2)

  U'(-5,-2)

  V'(-7,-7)

• S'(-1,7)

  T'(-3,2)

  U'(-5,2)

  V'(-7,7)

• S'(1,7)

  T'(3,2)

  U'(5,2)

  V'(7,7)

Give the coordinates of the image.

Triangle FGH with vertices F(-7,8), G(-1,1), and H(-8,4) :

Rotation of 270 degrees counterclockwise about the origin

• F'(-7,-8)

  G'(-1,-1)

  H'(-8,-4)

• F'(7,8)

  G'(1,1)

  H'(8,4)

• F'(-8,7)

  G'(-1,1)

  H'(-4,8)

• F'(8,7)

  G'(1,1)

  H'(4,8)

Give the coordinates of the image.

Square JKLM with vertices J(1,-3), K(5,0), L(8,-4), and M(4,-7) :

Rotation of 90 degrees counterclockwise about the origin

• J'(3,1)

  K'(0,5)

  L'(4,8)

  M'(7,4)

• J'(3,-1)

  K'(0,-5)

  L'(4,-8)

  M'(7,-4)

• J'(1,3)

  K'(5,0)

  L'(8,4)

  M'(4,7)

• J'(-1,3)

  K'(-5,0)

  L'(-8,4)

  M'(-4,7)

Give the coordinates of the image.

Trapezoid QRST with vertices Q(2,1), R(2,5), S(4,5), and T(8,1) :

Rotation of 90 degrees clockwise about the origin

• Q'(2,-1)

  R'(2,-5)

  S'(4,-5)

  T'(8,-1)

• Q'(-2,1)

  R'(-2,5)

  S'(-4,5)

  T'(-8,1)

• Q'(1,-2)

  R'(5,-2)

  S'(5,-4)

  T'(1,-8)

• Q'(-1,2)

  R'(-5,2)

  S'(-5,4)

  T'(-1,8)

Give the coordinates of the image.

Triangle MNP with vertices M(-7,6), N(-1,2), and P(-6,0) :

Rotation of 270 degrees clockwise about the origin

• M'(6,-7)

  N'(2,-1)

  P'(0,-6)

• M'(6,7)

  N'(2,1)

  P'(0,6)

• M'(-6,-7)

  N'(-2,-1)

  P'(0,-6)

Give the coordinates of the image.

Triangle XYZ with vertices X(4,7), Y(8,5), and Z(6,3) :

Rotation of 90 degrees counterclockwise about the point (1,2)

• X'(-4,5)

  Y'(-2,9)

  Z'(0,7)

• X'(4,-5)

  Y'(2,-9)

  Z'(0,-7)

• X'(-7,4)

  Y'(-5,8)

  Z'(-7,0)

• X'(7,-4)

  Y'(5,-8)

  Z'(7,0)

Give the coordinates of the image.

Rectangle CDEF with vertices C(-7,6), D(-4,6), E(-4,1), and F(-7,1) :

Rotation of 180 degrees about the point (-3,-1)

• C'(7,6)

  D'(4,6)

  E'(4,1)

  F'(7,1)

• C'(7,-6)

  D'(4,-6)

  E'(4,-1)

  F'(7,-1)

• C'(1,-8)

  D'(-2,-8)

  E'(-2,-3)

  F'(1,-3)

• C'(-8,1)

  D'(-8,2)

  E'(-3,-2)

  F'(-3,1)

Give the coordinates of the image.

Trapezoid QRST with vertices Q(3,1), R(5,2), S(10,0), and T(4,-3) :

Rotation of 270 degrees counterclockwise about the point (3,-4)

• Q'(8,-4)

  R'(9,-6)

  S'(7,-11)

  T'(4,-5)

• Q'(-4,8)

  R'(9,-6)

  S'(-11,7)

  T'(-5,4)

• Q'(1,-3)

  R'(2,-5)

  S'(0,-10)

  T'(-3,-4)

• Q'(-1,3)

  R'(-2,5)

  S'(0,10)

  T'(-3,4)

Give the coordinates of the image.

Square JKLM with vertices J(-3,5), K(0,8), L(3,5), and M(0,2) :

Rotation of 90 degrees clockwise about the point (-4,0)

• J'(1,-1)

  K'(4,-4)

  L'(1,-7)

  M'(-2,-4)

• J'(-5,-3)

  K'(-8,0)

  L'(-5,3)

  M'(-2,0)

• J'(-1,1)

  K'(-4,4)

  L'(-1,7)

  M'(2,4)

• J'(5,3)

  K'(8,0)

  L'(5,-3)

  M'(2,0)