Reflections and Rotation

In the figure, triangle PQR has vertices P(0, −1), Q(3, −1) and R(5, −3). What are the vertices of the image after the translation (x, y) → (x − 5, y + 1)?

• P′ (1, −6), Q′ (4, −6), R′ (6, −8)
• P′ (−5, 0), Q′ (−2, 0), R′ (0, −2)
• P′ (5, −2), Q′ (8, −2), R′ (10, −4)
• P′ (−1, 4), Q′ (2, 4), R′ (4, 2)

Triangle XYZ is translated so that X′ is at (4, –2). Which rule defines this translation?

• (x + 2, y – 6)
• (x – 6, y + 2)
• (2x, y – 6)
• (x – 2, y + 6)

Which reflection does the image show?

• Reflection across the x-axis according to the rule (x, y) → (x, −y)
• Reflection across the y-axis according to the rule (x, y) → (x, −y)
• Reflection across the x-axis according to the rule (x, y) → (−x, y)
• Reflection across the y-axis according to the rule (x, y) → (−x, y)

Triangle ABC is rotated 270° counterclockwise about the origin. Which is the algebraic rule applied to one of the vertices?

• (−1, −4) → (−4, 1)
• (−4, −1) → (−4 + 5, 1 + 3)
• (−4, 1) → (−1, −(−4))
• (−4, 1) → (1, −(−4))

How far has the figure been rotated?

• 45°
• 90°
• 180°
• 360°

The rectangle above is rotated 90° clockwise. Which shows the image of the rectangle after the rotation?

• Graph F
• Graph G
• Graph H
• Graph J

If you were to rotate ABCD 180°  about the origin, what would the coordinate of A' be?

• (-5, 5)
• (-3, -5)
• (-5, 3)
• (-3, 3)

Determine where x′ would be if you translated x three units to the left and two units down.

• (-4, 6)
• (-3, 1)
• (-4, 2)
• (-2, -4)

If the dotted figure is the image, the original figure was reflected over the ...

• x-axis
• y-axis

Which answer shows a reflection across the x-axis?

• d
• c
• b
• a