Chapter 3: Two and Three-Dimensional Transformation

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Questions

1. Define transformation.

   Or, What do you mean by geometric and coordinate transformation?

   Or, Briefly explain different types of transformation procedures.

   (Appeared in: 2009, 2010, 2011, 2014, 2015, 2021)

2. What is composite transformation? Explain with an example.

   (Appeared in: 2013, 2016)

3. Explain the basic transformations with diagrams.

   Or, Describe the process of rotation and scaling with respect to the origin of two-dimensional geometric transformation.

   Or, Describe different types of geometric transformations.

   (Appeared in: 2009, 2011, 2016) or, Define rotation and scaling. (2009)

4. Define:

   (a) Rotation

   (b) Translation (Appeared in: 2018, 2020)

   (c) Scaling

5. Differentiate between geometric and coordinate transformation.

   (Appeared in: 2010, 2014, 2020, 2021)

6. Define mirror reflection.

   (Appeared in: 2009)

7. Write an algorithm for the transformation matrix that reflects an object about a line.

8. What is 2D Discrete Cosine Transformation (DCT)?

   Or, Define DCT and explain it briefly.

   (Appeared in: 2009, 2010, 2018, 2019)

9. Derive the transformation that relates an object’s point rotated by 9° about the origin.

   • Write the matrix representation for this relation.
   • Find the matrix that represents the rotation of an object by 30° about the origin.(Appeared in: 2009)

10. Magnify the triangle with vertices A(0, 0), B(1, 1), and C(5, 2) to twice its size while keeping C(5, 2) fixed.

11. Perform a 45° rotation of the triangle A(0, 0), B(1, 1), and C(5, 2):

    • (a) About the origin.
    • (b) About P(-1, -1). (Appeared in 2013, 2016, 2017, 2018, 2020)

12. Deduce the formula for three-dimensional geometric transformations of translation, scaling, and rotation.

13. Explain three-dimensional geometric transformation in detail.

    (Appeared in: 2012, 2017)

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