Rotations, Dilations, and Sequences

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.

• 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)

Which describes a possible sequence of transformations that takes polygon GHJK to polygon G'H'J'K' ?

• a 180-degree rotation, followed by a dilation centered at the origin with scale factor of 1/2

• a reflection across the line y=x, followed by a dilation centered at the origin with a scale factor of 2

• a reflection across the y-axis, followed by a reflection across the x-axis, followed by a dilation with scale factor 2

• a reflection across the y-axis, followed by a translation down 10 units, followed by a dilation centered at the origin with a scale factor of 1/2

• X'(9,6)

• Y'(0,9)

• X'(-9,-6)

• Z'(6,-3)

Rotate 90 degrees counterclockwise AND translate down 2 units

• 
• 
• 

Which sequence of transformations will get you from triangle ABC to its image triangle A'B'C'?

• Reflection, then a translation

• Rotation, then a dilation

• Reflection, then a rotation

• Dilation, then a reflection

• Rotation, then rotation

• rotation, then dilation

• translation, then reflection

• reflection, then rotation

What sequence of transformations could map triangle ABC to triangle A"B"C"?

• A dilation followed by a rotation.

• A translation followed by a reflection.

• A rotation about the origin followed by a translation.

• A reflection followed by a rotation.