Test Questions on Properties and Performing Reflections (Grade 8)

📚 Quick Study Guide

• 📏 Properties of Reflections: Reflections create a mirror image across a line (the line of reflection). The image is congruent to the original.
• 📐 Line of Reflection: The line of reflection is the perpendicular bisector of the segment joining a point and its image.
• 📍 Coordinates & Reflections:
  • Reflecting over the x-axis: $(x, y) \rightarrow (x, -y)$
  • Reflecting over the y-axis: $(x, y) \rightarrow (-x, y)$
  • Reflecting over the line $y = x$: $(x, y) \rightarrow (y, x)$
  • Reflecting over the line $y = -x$: $(x, y) \rightarrow (-y, -x)$
• ➕ Congruence: Reflections preserve size and shape, meaning the pre-image and image are congruent.

Practice Quiz

1. What happens to the y-coordinate when a point is reflected over the x-axis?
   1. It stays the same.
   2. It becomes its opposite.
   3. It becomes x.
   4. It becomes 0.
2. A triangle has vertices A(1, 2), B(3, 4), and C(5, 2). If it is reflected over the y-axis, what are the coordinates of A'?
   1. (1, -2)
   2. (-1, 2)
   3. (-1, -2)
   4. (2, -1)
3. If a point (4, -3) is reflected over the line y = x, what are the coordinates of its image?
   1. (-3, 4)
   2. (-4, 3)
   3. (3, -4)
   4. (-3, -4)
4. Which transformation preserves the size and shape of a figure?
   1. Dilation
   2. Reflection
   3. Reduction
   4. Enlargement
5. The point (2, 5) is reflected over the line y = -x. What are the coordinates of the reflected point?
   1. (5, 2)
   2. (-5, -2)
   3. (-2, -5)
   4. (-2, 5)
6. What is the line of reflection if point P(3,7) becomes P'(3,-7)?
   1. x-axis
   2. y-axis
   3. y = x
   4. y = -x
7. A square with vertices at (1,1), (1,4), (4,4), and (4,1) is reflected over the line x = 5. What are the coordinates of the reflected image of the point (1,1)?
   1. (9,1)
   2. (1,9)
   3. (4,4)
   4. (4,1)