GEOMETRICAL TRANSFORMATION REVISION QUESTIONS WITH ANSWERS

Geometrical Transformation Questions

1. Define a transformation in geometry.

2. What are the four basic types of transformations?

3. Describe a translation and give an example.

4. Translate the point \(A(2, 3)\) by the vector \(\begin{pmatrix}4\\-2\end{pmatrix}\).

5. What is the effect of translation on shape and size?

6. Define rotation in geometry.

7. Rotate the point \(B(1, 2)\) \(90^\circ\) clockwise about the origin.

8. What is the center of rotation?

9. What are the properties of a shape after rotation?

10. Define reflection and its effect on coordinates.

11. Reflect the point \(C(4, -3)\) in the y-axis.

12. What is the line of reflection?

13. Describe an enlargement (dilation) and its center.

14. Enlarge the triangle with vertices \((1, 2)\), \((2, 3)\), and \((3, 1)\) by scale factor 2 about the origin.

15. What happens to the angles and side lengths during enlargement?

16. What is an invariant point under a transformation?

17. Give an example of a transformation with all points invariant.

18. State whether enlargement is an isometry.

19. Which transformations preserve orientation?

20. A shape is rotated \(180^\circ\) about the origin. What happens to its coordinates?

21. What is a matrix representation of a transformation?

22. What is the matrix for reflection in the x-axis?

23. Use matrix \(\begin{pmatrix}0 & -1\\ 1 & 0\end{pmatrix}\) to rotate a point \(D(1, 0)\). What is the image?

24. Differentiate between direct and opposite transformations.

25. What type of transformation maps a triangle onto itself?

26. What is a glide reflection?

27. Reflect the point \(E(-2, 5)\) in the line \(y = x\).

28. Is rotation an example of rigid transformation?

29. What transformation maps the point \(F(0, 1)\) to \((-1, 0)\)?

30. Which transformations are considered isometries?

Answers

1. A movement of a shape from one position to another.
2. Translation, rotation, reflection, and enlargement.
3. Slides a shape without turning or flipping it.
4. \(A'(6, 1)\)
5. Shape and size remain the same.
6. Turning a shape around a fixed point.
7. \(B'(2, -1)\)
8. The point about which a figure rotates.
9. Shape, size, and orientation preserved (if center is origin).
10. Flips a figure over a line, mirror image.
11. \(C'(-4, -3)\)
12. The line over which the reflection is made.
13. Resizing a shape about a fixed point.
14. \((2, 4), (4, 6), (6, 2)\)
15. Angles stay same; side lengths change proportionally.
16. A point that maps to itself.
17. Identity transformation.
18. No, it changes size.
19. Translation and rotation.
20. Both coordinates change sign: \((-x, -y)\)
21. A matrix that represents movement or resizing of a figure.
22. \(\begin{pmatrix}1 & 0\\ 0 & -1\end{pmatrix}\)
23. \((0, 1)\)
24. Direct keeps orientation; opposite reverses it.
25. Identity transformation or rotation by \(360^\circ\).
26. Reflection followed by a translation.
27. \((5, -2)\)
28. Yes.
29. Rotation \(90^\circ\) clockwise about origin.
30. Translation, rotation, and reflection.