Worksheet Chapter 11: Isometric Transformations

1. A shape undergoes two successive transformations: First, a reflection in the x-axis, then a 180° rotation about the origin O(0,0). (a) Find the final coordinates of point Q(3, -4) after both transformations. (b) Describe a single simple transformation that achieves the same result as these two combined.

2. Point B(4, -1) is mapped to B'(-1, -4) under a rotation about origin O(0,0). State the angle and direction of rotation.

3. True or False: The order of rotational symmetry of a square is 4.

4. Fill in the blank: An isometric transformation preserves both the ________ and size of an object.

5. Triangle ABC has vertices A(1, 2), B(4, 2), and C(1, 6). (a) Find the coordinates of triangle A'B'C' under translation (-3, 4)^T. (b) Calculate the length of side A'C'.

6. Which of the following transformations maps point P(2, 3) to P'(-2, 3)?

7. Vertices of square PQRS are P(1, 1), Q(3, 1), R(3, 3), and S(1, 3). (a) Find the coordinates of P'Q'R'S' under a 90° counterclockwise rotation about origin O(0,0). (b) Calculate the area of P'Q'R'S'. (c) State whether PQRS and P'Q'R'S' are congruent, giving a reason.

8. Find the image of point A(-3, 7) under the translation vector (5, -2)^T.

9. True or False: A reflection changes the orientation of an object.

10. Point P(-2, 5) undergoes a reflection in line x = 1 to form image P1, followed by a translation (2, -3)^T to form image P2. Find: (a) Coordinates of P1. (b) Coordinates of P2.