Lesson 4: Revision and Practice

🟦 Introduction

Congratulations! 🎉 You’ve now explored three powerful topics: Rigid Motions (translation, reflection, rotation), Enlargement and Similar Figures, and Constructions and Loci. This final lesson is your opportunity to revise everything you’ve learned and test your understanding through mixed exercises and word problems. Let’s sharpen those geometry tools and tackle real exam-style challenges together!

🟩 Quick Concept Recap

🔹 Rigid Motion Summary

🔹 Enlargement and Similar Figures

• Enlargement changes size, not shape.
• Similar figures have equal angles and proportional sides.
• Formula for image side:

🔹 Constructions and Loci

• Use only a ruler and compass to construct perpendicular bisectors, angle bisectors, etc.
• Loci describe a set of points that follow a rule (e.g., fixed distance from a point = circle).

🟨 Practice Exercises

📘 Section A: Mixed Transformations

1. Translate point A(2, 3) 4 units right and 2 units down. What are the new coordinates?
2. Reflect point B(−5, 1) over the x-axis.
3. Rotate point C(0, 6) 90° clockwise about the origin. Give the new coordinates.
4. Which transformation does NOT change the size or shape of a figure but changes its orientation?

📘 Section B: Enlargement & Similar Figures

1. A triangle has sides 3 cm, 4 cm, and 5 cm. It is enlarged by scale factor 2. What are the side lengths of the image?
2. Triangle X has sides 5 cm, 6 cm, and 7 cm. Triangle Y has sides 10 cm, 12 cm, and 14 cm. Are they similar? Why?
3. The side of a square becomes 18 cm after enlargement. If the scale factor was 3, what was the original side?

📘 Section C: Constructions and Loci

1. Draw a line segment of 7 cm and construct its perpendicular bisector.
2. Given two points P and Q, construct the locus of points equidistant from them.
3. A point moves so that it is always 2 cm from line AB. Describe and sketch the locus.

📘 Section D: Word Problems

1. A school is designing a circular garden such that the center is a tree and the path is always 4 m away from the tree. What shape does the path form? What construction can be used to draw it?
2. An architect reflects the front view of a building across a vertical axis to create symmetry. What transformation is this? What remains unchanged?

✅ Answers and Explanations

Section A:

1. (6, 1)
2. (−5, −1)
3. (6, 0)
4. Reflection

Section B:

1. 6 cm, 8 cm, 10 cm
2. Yes – all sides are in the same ratio (×2), and shape is preserved
3. 18 ÷ 3 = 6 cm

Section C:

1. 1. Student should construct perpendicular bisector (label as locus)

• Construct two points P and Q, construct the locus of points equidistant from them.
  
• Two parallel lines, 2 cm above and below AB

Section D:

1. The path forms a circle. Use a compass to construct it.
2. Reflection; shape and size stay the same

🔁 Recap

You’ve now practiced all key transformation tools: sliding, flipping, turning, enlarging, constructing, and tracing loci. These concepts show up often in BECE and in real life — from art design to engineering. The more you practice them, the more confident you’ll become at solving any geometry challenge thrown your way!

🪞 Reflection Prompt

If you could design a park, where would you use reflection or enlargement? How could loci help plan paths, fountains, or fences?