Worksheet Chapter 5: Congruency, Enlargement and Combined Transformations

1. 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''.

2. 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.

3. 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.

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

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

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

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

8. 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.

9. 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'.

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