Constructing a scale drawing including choosing a suitable scale, converting between scaled and real distances, and planning a navigation course using three-figure bearings and distances.

What this dot point is asking

The SQA wants you to construct a scale drawing and choose a suitable scale, convert between scaled and real distances, and plan a navigation course using three-figure bearings measured clockwise from north, together with distances.

Scale and scale drawings

A scale links a length on a drawing or map to the real length it represents. It is written as a ratio such as $1 : 100$, meaning one unit on the drawing equals $100$ of the same units in reality. The two numbers in the ratio have no units of their own, so the same scale works whether you measure in centimetres or millimetres, as long as both sides are read in the same unit. A scale can also be written in words, such as "$1$ cm represents $5$ km", which is often clearer for a map.

When you construct a scale drawing, choose a scale so the whole object fits the page but is still large enough to read; for example, a $20$ m room drawn at $1 : 200$ becomes a $10$ cm line, which fits comfortably. A scale that is too large runs off the page, while one that is too small makes the drawing hard to measure, so the choice itself is part of the answer. Once drawn, any length can be measured on the drawing and scaled up to find the real distance, which is how scale drawings are used to solve a problem rather than just to illustrate it.

Bearings and navigation

A bearing gives a direction as an angle measured clockwise from north. It is always written with three figures, so a direction of forty degrees is $040^\circ$ and due south is $180^\circ$.

Examples in context

Scale drawings and navigation appear in map reading, planning a garden or room layout, sailing and walking routes, and flight paths. Each rests on applying a scale the right way round, converting units carefully, and measuring bearings clockwise from north in three figures, the skills here. A poorly chosen scale either runs off the page or is too small to read, so the choice of scale is itself assessed.

A return bearing, the direction back the way you came, is the original bearing plus or minus $180^\circ$: if the outward bearing is $070^\circ$, the return is $070 + 180 = 250^\circ$. This back-bearing idea is useful when a navigation course needs to return to its start, and it reinforces that bearings are always measured clockwise from north.

Try this

Q1. On a $1 : 25\,000$ map, two points are $6$ cm apart. Find the real distance in kilometres. [3 marks]

• Cue. $6 \times 25000 = 150000$ cm $= 1.5$ km.

Q2. Write a bearing of due west in three figures. [1 mark]

• Cue. $270^\circ$.

Q3. A scale is $1$ cm to $2$ km. How long is a $9$ km leg on the drawing? [2 marks]

• Cue. $9 \div 2 = 4.5$ cm.