Grade 9 Scale Drawings: Short Notes

9 ශ්‍රේණිය · 3 වාරය · 27 පරිච්ඡේදය · පරිමාණ රූප

43%

of Grade 9 term tests include it (17 of 40)

124

marks in past papers (22 questions)

11 min

full lesson with quick checks

🎯 What you'll learn

Give the direction of a place using compass points and bearings
Find back bearings
Use a scale written in words or as a ratio to find actual and drawing lengths
Draw a scale diagram from bearings and distances, and read lengths and bearings from it

Where is the boat?

A fishing boat off Negombo radios the harbour: "We are 12 km from the lighthouse, on a bearing of 060°." With just those two facts the coast guard can mark the boat's exact spot on a map. Directions plus distances plus a good scale drawing: that's this lesson.

Compass directions

The four main directions are North, East, South, West, each 90° apart going clockwise.Halfway between them are NE, SE, SW, NW, at 45° to the main directions.On maps and in scale drawings, North points up unless the question says otherwise.

What is a bearing?

The bearing of B from A is the angle measured:1. at A, the point you are 'from',2. starting from the North direction,3. turning clockwise until you face B.Write it with three digits: 060°, 135°, 270°. East is 090°, South 180°, West 270°.

Two bearings

Left: the bearing of B from A is 060°. Right: the bearing of D from C is 230°. Always start at North and turn clockwise, even past 180°.

Turning round: the back bearing

If the bearing of B from A is known, the bearing of A from B points the opposite way, so it differs by 180°.• If the bearing is less than 180°, add 180°.• If it is 180° or more, subtract 180°.Example: B from A is 060°, so A from B is 060° + 180° = 240°.

✏️ Back bearings

(i) The bearing of a bus stand from a school is 115°. Find the bearing of the school from the bus stand.(ii) The bearing of a well from a house is 300°. Find the bearing of the house from the well.

1(i) 115° is less than 180°, so add: 115° + 180° = 295°.
2(ii) 300° is more than 180°, so subtract: 300° − 180° = 120°.
3Sketch both to check: each pair points in opposite directions.

✅ (i) 295° (ii) 120°

⚠️ From where, and which way?

Common slips with bearings:• Measuring anticlockwise, or starting from East instead of North.• Drawing the North line at the wrong point. In "the bearing of B from A", the North line and the angle go at A.• Writing 60° instead of 060°.• For a back bearing, forgetting to add or subtract 180°.

Scale

A scale drawing is an accurate drawing with every length reduced in the same ratio. Angles stay the same.A scale can be written two ways:• 1 cm represents 50 m• as a ratio, 1 : 5000 (since 50 m = 5000 cm)Actual length = drawing length × scale factor. Drawing length = actual length ÷ scale factor.

✏️ Reading a map

On a map with scale 1 : 50 000, the road from Kurunegala town to a reservoir measures 6.4 cm. Find the actual distance in km.

1Actual = 6.4 × 50 000 = 320 000 cm
2÷ 100 for metres: 3200 m
3÷ 1000 for kilometres: 3.2 km

✅ 3.2 km

⚠️ Units, units, units

A ratio scale like 1 : 2000 compares the same units: 1 cm to 2000 cm, not 2000 m. Many wrong answers come from skipping the conversion.• cm → m: ÷ 100• m → km: ÷ 1000• cm → km: ÷ 100 000Write the unit at every step.

Drawing a scale diagram

1. Make a rough sketch with all the data.2. Choose a sensible scale (e.g. 1 cm represents 1 km).3. Draw a North line at the start; use a protractor to mark the bearing clockwise.4. Measure the scaled distance along it.5. At each new point draw a new North line (parallel to the first) and repeat.6. Measure the length or angle you need, and convert back.

📌 Remember

• Bearing: from North, clockwise, three digits, measured at the 'from' point.• Back bearing: add 180° if under 180°, else subtract 180°.• Scale 1 : n means 1 cm represents n cm.• Actual = drawing × n; convert units at the end.• In a scale drawing, draw a new North line at every point.

🧾 Quick revision sheet

How is a bearing measured?	From North, clockwise, written with three digits.
Bearing of East, South and West	090°, 180°, 270°
Bearing of NE and of NW	045° and 315°
Bearing of B from A is 070°. Bearing of A from B?	250° (070° + 180°)
Meaning of the scale 1 : 1000	1 cm on the drawing represents 1000 cm = 10 m.
cm to km	Divide by 100 000
Does a scale drawing change angles?	No. Lengths are scaled; angles stay the same.