28.8. Geometrical Interpretation of Linear Transformations

Try these first

1. 1.

   Define a linear transformation. Provide an example.

   Hint

   Think of transformations used in CAD programs.

2. 2.

   What does scaling do to a vector?

   Hint

   Consider enlarging or reducing the size of objects.

3. 3.

   What is an example of a linear transformation?

   • Reflection
   • Shading
   • None of the above

   Hint

   Remember types of transformations we discussed.

4. 4.

   True or False: Scaling can change a vector’s direction.

   • True
   • False

   Hint

   Think about what happens during resizing.

5. 5.

   You have a square with vertices at (1,1), (1,-1), (-1,-1), and (-1,1). If you apply a scaling transformation with a factor of 2, what are the new vertices?

   Hint

   Multiply each vertex coordinate by the scaling factor.

6. 6.

   Describe how reflection over the x-axis changes a triangle with vertices at (0,3), (2,1), and (1,2). What are the new coordinates?

   Hint

   Focus on how the y-values change during reflection.