Worksheet Chapter 5: Congruency, Enlargement and Combined Transformations

1. In a diagram, region B is the image of region A under an enlargement centered at point (1, 2) with a scale factor of k = -2. Given that the area of region A is 24 cm², calculate (a) the area of region B, and (b) the area of the total combined region formed by region A and region B.

2. Fill in the blank: A transformation that preserves both shape and size is known as an ________.

3. Which of the following scale factors produces an image that is smaller than the original object and inverted relative to the center of enlargement?

4. A polygon has an area of 36 cm². Under an enlargement, the area of its image is 324 cm². Calculate the positive scale factor k of the enlargement.

5. Triangle ABC is enlarged to triangle A'B'C' with a scale factor of k = 4. If the side length AB is 5 cm, calculate the length of side A'B'.

6. A rectangle with an area of 18 cm² undergoes an enlargement with a scale factor of k = 3. Calculate the area of the resulting image.

7. True or False: In a combined transformation AB, transformation A is performed first, followed by transformation B.

8. Point P(3, 7) is reflected across the y-axis to obtain point P'. Point P' is then translated by vector (2, -4) to obtain point P''. State the coordinates of P' and P''.

9. True or False: The Angle-Angle-Angle (AAA) condition is a valid criterion to prove that two triangles are congruent.

10. State the three core single transformations that are classified as isometric transformations.