Test Your Knowledge: Understanding Reflections 8th Grade Math Assessment

📚 Quick Study Guide

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• Reflection: A transformation that flips a figure over a line, called the line of reflection.
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• Line of Reflection: The line across which a figure is reflected. Common lines of reflection are the x-axis ($y = 0$) and the y-axis ($x = 0$).
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• Reflection over the x-axis: The rule is $(x, y) \rightarrow (x, -y)$. The x-coordinate stays the same, and the y-coordinate changes sign.
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• Reflection over the y-axis: The rule is $(x, y) \rightarrow (-x, y)$. The y-coordinate stays the same, and the x-coordinate changes sign.
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• Important properties: Reflections preserve distance and angle measure. The image is congruent to the pre-image.

Practice Quiz

1. What is the image of point (3, -2) after a reflection over the x-axis?
   1. (3, 2)
   2. (-3, -2)
   3. (-3, 2)
   4. (2, -3)
2. What is the image of point (-1, 4) after a reflection over the y-axis?
   1. (1, 4)
   2. (-1, -4)
   3. (1, -4)
   4. (-1, 4)
3. If a point (a, b) is reflected over the x-axis, which of the following is the correct image?
   1. (-a, b)
   2. (a, -b)
   3. (-a, -b)
   4. (b, a)
4. A triangle has vertices A(0, 0), B(2, 0), and C(1, 3). What are the coordinates of vertex C after a reflection over the y-axis?
   1. (-1, -3)
   2. (1, -3)
   3. (-1, 3)
   4. (1, 3)
5. Which transformation represents a reflection over the line y = 0?
   1. (x, y) → (-x, y)
   2. (x, y) → (x, -y)
   3. (x, y) → (-x, -y)
   4. (x, y) → (y, x)
6. The point (5, -1) is reflected over the y-axis. What quadrant does the image lie in?
   1. Quadrant I
   2. Quadrant II
   3. Quadrant III
   4. Quadrant IV
7. A square has vertices at (1,1), (1,3), (3,3), and (3,1). If it is reflected over the x-axis, what is the new coordinate of the vertex that was originally at (1,3)?
   1. (1,-3)
   2. (-1,3)
   3. (-1,-3)
   4. (3,-1)