Congruent Figures and Sequences of Transformations

Which series of transformations were performed in the figure?

• Translation 5 units down, reflection over the y-axis

• Reflection over the x-axis, translation 6 units right

• Rotation 90^o clockwise, reflection over the x-axis

• Rotation 180^o clockwise, reflection over the y-axis

Which of the statements is true about the graphed triangles?

• They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 2.
• They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.
• They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 2.
• They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

Rectangle ABCD is undergoing a series of transformations. Which of the following transformations will NOT cause the resulting rectangle  to maintain congruence with rectangle ABCD? 

• Translation 3 units left, then translation 7 units down. 
  
• Dilation by a scale factor of 3, then dilation by a scale factor of 3.
• Dilation by a scale factor of 2, then dilation by a scale factor of 1/2.
• Translation 4 units right, then translation 6 units up. 

Squares K and P are similar. Which series of transformations of square K show that K and P are similar?

• Rotation 90 degree, then dilation by a scale factor of 0.5.
  
• Rotation 45 degree, then dilation by a scale factor of 0.5.
• Reflection over a vertical axis, then dilation by a scale factor of 0.5.
• Reflection over a horizontal axis, then dilation by a scale factor of 0.5
  

Figures ABC and DEF are similar.  Which series of transformations of figure ABC shows that ABC and DEF are Similar? 

• 90 degree clockwise rotation, then dilation by a scale factor of ¾
  
• 90 degree counterclockwise rotation, then dilation by a scale factor of ¾
  
• Reflection across a vertical line, then dilation by a scale factor of ¾
• Reflection across a horizontal line, then dilation by a scale factor of ¾
  

Which of the following describes the sequence of transformations shown?

• Reflect across the x-axis and then rotate -90 degrees cw around the origin

• Rotate 90 degrees cw around the origin and then translate down.

• Reflect across the x-axis and then reflect across the y-axis.

• Translate up and then rotate 90 degrees ccw about the origin.

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)
• A'(6,6) B'(9,9) C'(12,6)
• A'(0,0) B'(3,3) C'(6,0)
• A'(1,1) B'(2,2) C'(3,1)

Which is an Example of a dilation

• 
• 
• 
• 

Which rule shows the transformation?

• (x, y) ----> (0.5x, 0.5y)
• (x, y) ----> ( 2 + x, 2 + y)
• (x, y) -----> (2x, 2y)
• (x, y) -----> (3x, 3y)

Under what composition of transformations does triangle ABC map onto triangle A''B''C''

• Reflection over x-axis, then Rotation of 90 Degrees

• Rotation of -90 Degrees, then Reflection over y-axis

• Reflection over y-axis, then Rotation of -90 Degrees

• Rotation of 90 Degrees, then Reflection over x-axis