GRADE 9 Mathematics GEOMETRY – SCALE DRAWING Notes

Mathematics — Geometry

Subtopic: Scale Drawing (Age ~14, Kenyan context)

Learning goals

• Understand what a scale is and how to read it (e.g. 1:50, 1:100).
• Convert between actual (real) sizes and drawing (plan) sizes using scale.
• Draw or measure objects accurately using a given scale and use a scale bar.

Key vocabulary

• Scale: a ratio that shows how drawing size relates to real size (example: 1:100).
• Scale factor: the multiplier used when going from drawing to real or real to drawing.
• Enlargement and Reduction: making a drawing bigger or smaller than the real object.
• Scale bar: a small ruler on the drawing that shows length units at the chosen scale.

What does a scale 1:100 mean?

1 unit on the drawing represents 100 of the same units in real life. Example: 1 cm on the plan = 100 cm (1 m) in real life.

Important: units must match

Always convert lengths to the same units before you use the scale. If the real length is in metres, convert to centimetres if you will measure in centimetres on the drawing (or convert drawing units to metres).

How to convert sizes (step-by-step)

1. Write the scale as a ratio. Example: 1:100 (one on the drawing = one hundred in reality).
2. To find drawing size from real size: drawing = real ÷ scale (if scale is 1:n then drawing = real ÷ n).
3. To find real size from drawing: real = drawing × n (if scale is 1:n).
4. Keep units the same (convert m → cm or cm → m as needed).

Visual example (Actual room → plan at 1:100)

Actual room: 6 m by 4 m. Scale: 1:100. Convert metres to centimetres first:

6 m = 600 cm, 4 m = 400 cm. Drawing size = real cm ÷ 100 → 600÷100 = 6 cm and 400÷100 = 4 cm.

Worked examples

Example 1 — Plan of classroom
A classroom is 8 m long and 6 m wide. Draw a plan at scale 1:100. What will be the length and width on the drawing?

Solution:

1. Convert to cm: 8 m = 800 cm, 6 m = 600 cm.
2. Drawing size = real cm ÷ 100. So length = 800 ÷ 100 = 8 cm; width = 600 ÷ 100 = 6 cm.
3. Answer: plan = 8 cm by 6 cm.

Example 2 — Map distance
On a map with scale 1:250 000, the distance between two towns is 2 cm on the map. How far apart are the towns in kilometres?

Solution:

1. Real distance (cm) = map distance × 250 000 = 2 × 250 000 = 500 000 cm.
2. Convert cm to km: 100 000 cm = 1 km. So 500 000 cm = 5 km.
3. Answer: 5 km apart.

Example 3 — Find the scale factor
A model car is 1:25 scale. The real car is 4 m long. How long is the model in centimetres?

Solution:

1. Real length = 4 m = 400 cm.
2. Scale 1:25 means drawing/model = real ÷ 25 = 400 ÷ 25 = 16 cm.
3. Answer: model car is 16 cm long.

Tips and reminders

• When scale is written as 1:n: drawing length = real length ÷ n; real length = drawing length × n.
• Always convert all lengths to the same units before calculating (use cm for small plans, km for large maps).
• Write the units on your final answer and label the drawing with its scale.
• Use a scale bar on your drawing — it helps others read distances without recalculating.
• For enlargements (e.g. scale 2:1), multiply real size by 2. For reductions (e.g. 1:50), divide real size by 50.

Practice questions

1. A football pitch is 100 m by 64 m. Draw a plan at 1:500. What are the plan dimensions in centimetres?
2. On a road map scale 1:200 000, two towns are 3.5 cm apart on the map. Find the real distance in kilometres.
3. A scale model house is made at 1:100. If the real house height is 9 m, how tall is the model in centimetres?
4. A garden is 12 m by 5 m. On a plan at 1:50 what are the plan measurements (in cm)?
5. Explain how you would draw a rectangular kiosk 3 m by 2 m at scale 1:25. (Give step-by-step).

Answers to practice

1. 100 m = 10 000 cm; 64 m = 6 400 cm. Plan sizes = 10 000 ÷ 500 = 20 cm and 6 400 ÷ 500 = 12.8 cm → 20.0 cm by 12.8 cm.
2. Real distance = 3.5 × 200 000 cm = 700 000 cm = 7 km (since 100 000 cm = 1 km).
3. 9 m = 900 cm. Model height = 900 ÷ 100 = 9 cm.
4. 12 m = 1 200 cm → 1 200 ÷ 50 = 24 cm. 5 m = 500 cm → 500 ÷ 50 = 10 cm. Plan = 24 cm by 10 cm.
5. Steps: convert metres to cm (3 m = 300 cm, 2 m = 200 cm). Drawing size = real cm ÷ 25 → 300÷25 = 12 cm and 200÷25 = 8 cm. Draw rectangle 12 cm by 8 cm, add scale label "1:25" and a small scale bar (e.g. 1 cm = 0.25 m).

If you want, I can make printable A4-size working templates (with scale bars) for a few common scales used in Kenya (for example 1:50, 1:100, 1:500, 1:250 000).