Transformational Geometry

This coordinate grid shows triangle ABC and its image triangle A'B'C'. Which best describes the transformation used to create triangle A'B'C?

• Translated 5 units right and 9 units down
• Reflection over the x-axis
• Rotated 180 degrees clockwise
• Rotated 270 degrees counterclockwise

Identify the scale factor. (8.CC)

• 1/8

• 8

• 2

• 1/2

Which of the following statements is true?  (8.10A)

• A reflection over the x-axis will preserve the orientation of the pre-image figure but not the size.
• A 180° rotation clockwise is the same as a 180° counterclockwise rotation.
• A dilation will preserve the size but not the orientation of the figure. 
• A translation will preserve a figure’s orientation but not the size.

Which proportion is true? (8.3A)

(8.10B) To preserve the congruence of an image means to

• change the shape and size

• rotate the figure

• remain the same size

• reflect the figure

To change the orientation of an image means to

• change the way a figure is facing

• change the size of a figure

• change the shape of a figure

• slide across the y-axis

Jamal went to an amusement park. From the main entrance he used the algebraic representation  (x, y) → (x – 14, y + 5) to walk to a ride. Which ride did Jamal walk to? (8.10 C)

• Ride 1
• Ride 2
• Ride 3
• Ride 4

Triangle ABC is dilated by a scale factor of 3. Which is an algebraic representation of the dilation? (8.3C)

• (3x, 3y) → (x, y)
• (x, y) → (x+3, y-3)
• (x, y) → (0.33x, 0.33y)
• (x, y) → (3x, 3y)

Which algebraic representation describes the transformation from trapezoid WXYZ to trapezoid W'X'Y'Z'? (8.10 C)

• (x, y) → (x + 1, y + 2)
• (x, y) → (x – 1, y + 2)
• (x, y) → (–x, 2y)
• (x, y) → (–x + 2, y – 1)

A triangle has vertices J(−2, 9), K(2, −3), and L(−4, 5). The triangle is dilated so that vertex J′ has coordinates (-10, 45). Which algebraic representation represents the dilation? (8.10C)

• (x, y) → (5x, 5y)

• (x, 2y) → (2x, y)

• (x, y) → (4x, 4y)

• (8x, y) → (x, 8y)