Solved Examples of Multiple Geometric Transformations for Grade 8

📚 Quick Study Guide

• 📐 Translation: A transformation that slides a figure without changing its size, shape, or orientation. Every point of the figure moves the same distance and in the same direction.
• 🔄 Rotation: A transformation that turns a figure about a fixed point (center of rotation). It's defined by the angle and direction of rotation (clockwise or counterclockwise).
• mirror: Reflection: A transformation that flips a figure over a line (line of reflection), creating a mirror image.
• 📈 Dilation: A transformation that changes the size of a figure by a scale factor. If the scale factor is greater than 1, the figure enlarges; if it's between 0 and 1, the figure shrinks.
• ➕ Combining Transformations: Performing multiple transformations in sequence. The order matters!
• ✍️ Isometry: Transformations that preserve size and shape (translation, rotation, reflection). Dilation is not an isometry.
• 🧭 Coordinate Plane: Transformations can be easily described using coordinates. For example, a translation of $(x, y)$ to $(x+a, y+b)$.

Practice Quiz

1. Question 1: A triangle is translated 3 units to the right and 2 units up. If a vertex of the original triangle was at (1, 1), what are the coordinates of the corresponding vertex in the translated triangle?
   1. (2, -2)
   2. (4, 3)
   3. (-2, -1)
   4. (3, 4)
2. Question 2: A square is rotated 90 degrees clockwise about the origin. If one of its vertices was at (2, 0), what are the coordinates of this vertex after the rotation?
   1. (0, 2)
   2. (0, -2)
   3. (-2, 0)
   4. (2, 2)
3. Question 3: A point at (3, -2) is reflected over the x-axis. What are the coordinates of the reflected point?
   1. (-3, -2)
   2. (3, 2)
   3. (-3, 2)
   4. (-2, 3)
4. Question 4: A line segment has endpoints at (0, 0) and (2, 2). It is dilated by a scale factor of 2 with respect to the origin. What are the coordinates of the endpoints of the dilated line segment?
   1. (0, 0) and (1, 1)
   2. (0, 0) and (4, 4)
   3. (2, 2) and (4, 4)
   4. (4, 4) and (6, 6)
5. Question 5: A rectangle is first reflected over the y-axis and then translated 1 unit up. If a vertex of the original rectangle was at (2, -1), what are the coordinates of the corresponding vertex after both transformations?
   1. (-2, 0)
   2. (2, 0)
   3. (-2, -1)
   4. (0, -1)
6. Question 6: Which of the following transformations is NOT an isometry?
   1. Translation
   2. Rotation
   3. Reflection
   4. Dilation
7. Question 7: A triangle is rotated 180 degrees about the origin. If a vertex is at (-1, 4), what are the coordinates of the corresponding vertex after the rotation?
   1. (1, -4)
   2. (-1, -4)
   3. (1, 4)
   4. (4, -1)