Quiz on Translations Reflections Rotations Dilations

📚 Quick Study Guide

• 🔍 Translation: A slide of a figure. Every point moves the same distance in the same direction.
• ↔️ Reflection: A flip of a figure over a line (the line of reflection). The reflected image is a mirror image of the original.
• 🔄 Rotation: A turn of a figure around a fixed point (the center of rotation). Defined by the angle and direction of rotation.
• 📈Dilation: An enlargement or reduction of a figure. Defined by a scale factor. If the scale factor is greater than 1, it's an enlargement; if it's between 0 and 1, it's a reduction.
• 📐 Coordinate Rules:
  • Translation: $(x, y) \rightarrow (x+a, y+b)$, where $a$ and $b$ are the horizontal and vertical shifts, respectively.
  • Reflection over x-axis: $(x, y) \rightarrow (x, -y)$
  • Reflection over y-axis: $(x, y) \rightarrow (-x, y)$
  • Rotation 90° counterclockwise: $(x, y) \rightarrow (-y, x)$
  • Rotation 180°: $(x, y) \rightarrow (-x, -y)$
  • Dilation: $(x, y) \rightarrow (kx, ky)$, where $k$ is the scale factor.

Practice Quiz

1. A point (2, -3) is translated by (x, y) → (x - 4, y + 5). What are the coordinates of the image?

   1. (-2, 2)
   2. (6, -8)
   3. (2, -3)
   4. (-6, 8)

2. What are the coordinates of the image of point (4, 1) after a reflection over the x-axis?

   1. (-4, 1)
   2. (4, -1)
   3. (-4, -1)
   4. (1, 4)

3. A point (-1, 5) is rotated 90° counterclockwise about the origin. What are the coordinates of the image?

   1. (5, 1)
   2. (-5, -1)
   3. (-1, -5)
   4. (-5, 1)

4. Triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 1). If the triangle is dilated by a scale factor of 2, what are the coordinates of A'?

   1. (2, 4)
   2. (0.5, 1)
   3. (3, 4)
   4. (6, 8)

5. Which transformation preserves both the size and shape of a figure?

   1. Dilation
   2. Rotation
   3. All of the above
   4. None of the above

6. A line segment with endpoints (0, 0) and (2, 2) is reflected over the y-axis. What are the new endpoints?

   1. (0, 0) and (2, -2)
   2. (0, 0) and (-2, 2)
   3. (0, 0) and (-2, -2)
   4. (2, 2) and (0, 0)

7. What single transformation is equivalent to a reflection over the x-axis followed by a reflection over the y-axis?

   1. Translation
   2. Rotation of 90 degrees
   3. Rotation of 180 degrees
   4. Dilation