Worksheet Chapter 11: Isometric Transformations

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

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

3. 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'.

4. 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.

5. 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.

6. 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.

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

8. 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.

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

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