Grade 10 Math Transformations examples with solutions

📚 Quick Study Guide

• 🔍 Translation: A slide of the figure. Every point moves the same distance in the same direction. Represented as $(x, y) \rightarrow (x+a, y+b)$, where $a$ and $b$ are constants.
• 🔄 Rotation: A turn around a fixed point. Common rotations are 90°, 180°, and 270° clockwise or counterclockwise. Remember the rotation rules!
• reflection: A flip over a line. Common reflection lines are the x-axis ($y=0$) and the y-axis ($x=0$).
• 📏 Enlargement: Changes the size of the figure 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.
• ➕ Combinations: Transformations can be combined (e.g., a translation followed by a rotation). Apply them in the order specified!

Practice Quiz

1. What transformation is represented by $(x, y) \rightarrow (x-3, y+2)$?
   1. Translation
   2. Rotation
   3. Reflection
2. A point (2, -1) is reflected over the x-axis. What are the coordinates of the image?
   1. (2, 1)
   2. (-2, -1)
   3. (-2, 1)
3. A triangle is rotated 90° clockwise about the origin. What happens to a point (x, y)?
   1. (y, -x)
   2. (-y, x)
   3. (-x, -y)
4. What is the scale factor if a side of length 4 becomes a side of length 12 after an enlargement?
   1. 3
   2. 1/3
   3. 8
5. Which transformation does NOT preserve the size of the figure?
   1. Enlargement
   2. Translation
   3. Rotation
6. A point (5, 2) is translated by (1, -3) and then reflected across the y-axis. What is the final image?
   1. (-6, -1)
   2. (-4, -1)
   3. (6, -1)
7. A square with side length 2 is enlarged by a scale factor of 2. What is the area of the new square?
   1. 16
   2. 4
   3. 8