k = 3
Every image length is three times the original.
🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Define scale factor.
- Calculate scale factor from corresponding lengths.
- Use a scale factor to enlarge or reduce lengths.
- Distinguish enlargement from reduction.
🤔 Start with the Idea
A scale factor tells us how many times larger or smaller an image is than the original. It compares corresponding lengths.
📖 Linear Scale Factor
scale factor = image length ÷ original length
If the scale factor is greater than 1, the image is an enlargement. If it lies between 0 and 1, the image is a reduction.
k = 0.5
Every image length is half the original.
🎮 Try It Yourself
Change the corresponding lengths and watch the scale factor update.
🧠 Let’s Think Together
A model has length 18 cm. The real object has corresponding length 72 cm.
scale factor = 18 ÷ 72 = 0.25
The model is a reduction with scale factor 1/4.
✏️ Practice Questions
Build confidence- An original side is 5 cm and its image is 15 cm. Find the scale factor.
- A length of 24 cm is enlarged by scale factor 1.5. Find the image length.
- An image side is 8 cm after reduction by scale factor 0.4. Find the original side.
✅ Check your answers
- 3
- 36 cm
- 20 cm
⚠️ Common Mistakes
- Using different units on the two sides of a ratio scale.
- Multiplying when the question requires division, or dividing when it requires multiplication.
- Leaving out the unit or using a linear unit for an area.
- Rounding too early in a multi-step calculation.
🎯 Exam Focus
Write what the scale means before calculating. Show unit conversions clearly, keep full calculator values until the final step, and include the correct unit in the answer.
📌 One-Minute Summary
- A scale connects a drawing or model to the corresponding real object.
- Use multiplication when moving from a drawing measurement to a real measurement.
- Use division when working backwards from real size to drawing size.
- Ratio scales require the same unit on both sides.
- Area changes by the square of the linear scale factor.