Rotations, Dilations, and Sequences

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)

Give the coordinates of the image.

Quadrilateral ABCD with vertices A(-4,1), B(-2,3), C(0,-2), and D(-5,-2) :

Dilation where scale factor = 3

• A'(12,3)

  B'(6,9)

  C'(0,6)

  D'(15,6)

• A'(-12,3)

  B'(-6,9)

  C'(0,-6)

  D'(-15,-6)

• A'(3,-12)

  B'(9,-6)

  C'(-6,0)

  D'(-6,-15)

Give the coordinates of the image.

Triangle LMN with vertices L(2,-8), M(12,8), and N(14,-4) :

Dilation where scale factor = 1/2

• L'(-4,1)

  M'(4,6)

  N'(-2,7)

• L'(4,-16)

  M'(24,16)

  N'(14,-8)

• L'(1,-4)

  M'(6,4)

  N'(7,-2)

• L'(-16,4)

  M'(16,24)

  N'(-8,14)

Give the coordinates of the image.

Rhombus WXYZ with vertices W(2,-4), X(6,-2), Y(10,-4), and Z(6,-6) :

Dilation where scale factor = 3/2

• W'(3,-6)

  X'(9,-3)

  Y'(15,-6)

  Z'(9,-9)

• W'(-6,3)

  X'(-3,9)

  Y'(-6,15)

  Z'(-9,9)

• W'(-3,-6)

  X'(-9,-3)

  Y'(-15,-6)

  Z'(-9,-9)

• W'(-6,-3)

  X'(-3,-9)

  Y'(-6,-15)

  Z'(-9,-9)

Give the coordinates of the image.

Trapezoid DEFG with vertices D(-5,-15), E(10,10), F(10,5), and G(-5,0) :

Dilation where scale factor = 1/5

• D'(-5,-15)

  E'(10,10)

  F'(10,5)

  G'(-5,0)

• D'(3,-1)

  E'(2,2)

  F'(1,2)

  G'(0,-1)

• D'(-25,-75)

  E'(50,50)

  F'(50,25)

  G'(-25,0)

• D'(-1,-3)

  E'(2,2)

  F'(2,1)

  G'(-1,0)

Give the coordinates of the image.

Triangle XYZ with vertices X(-6,4), Y(0,6), and Z(-4,2) :

• X'(-9,6)

  Y'(-0,9)

  Z'(-6,3)

• X'(9,6)

  Y'(0,9)

  Z'(6,3)

• X'(9,-6)

  Y'(0,-9)

  Z'(6,-3)

• X'(-9,-6)

  Y'(0,-9)

  Z'(-6,-3)

Triangle DEF has vertices D(2,0), E(1,-2), and F(2,1). The triangle is rotated 90˚clockwise about the origin.What are the coordinates of vertex F' ?

• (-2, -1)

• (-1, -2)

• (1, -2)

• (-2, 1)

What sequence of transformations will get you from figure 1 to figure 3?

• reflection, then rotation

• rotation, then translation

• reflection, then translation

• Translation, then reflection

Which of the following sets of pre-images and images show a rotation?

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