Scale drawings.
Use a consistent scale and measure every bearing clockwise from the correct north line.
Draw and interpret scales · use three-figure and reverse bearings · combine bearings and distances
Convert every length with the same scale
A scale drawing is a small or large representation that preserves proportions. A scale gives a link between a drawing length and the corresponding real length.
Convert the stated scale into a useful matching pair, such as 1 cm representing 5 m. Decide whether you are moving from drawing to reality or reality to drawing, then multiply or divide accordingly. Only compare ratios directly after the units match.
A scale drawing keeps length ratios constant. Write the scale clearly and convert to matching units before using it.
A map has scale 1 : 25 000. A route is 7.2 cm on the map. Find the real distance.
For a real 3 km route, the map length is 300 000 ÷ 25 000 = 12 cm.
Pause and explainIf 1 cm represents 5 m, what real length does 3 cm represent?
15 m, because the drawing contains three copies of the scale’s 1 cm length.
Bearings start at north, not east
A bearing describes direction using a consistent reference: north at the starting point. Measure clockwise from that north line and write a three-figure angle.
The starting point matters. A bearing from A to B uses north at A; the reverse journey uses north at B and differs by 180°, adjusted into a full turn. Draw a north line at the correct location before measuring.
Forward bearing: 025°. Reverse bearing: 205°.
Use three figures: 025°, 090°, 180°, 270°. North is usually written 000° (a full turn is 360°). “D is due east of C” means the bearing of D from C is 090°.
The bearing of B from A is 025°. Find the bearing of A from B.
Reverse bearings differ by 180°. For a forward bearing of 250°, subtract 180° to obtain 070°.
Pause and explainWhy write a bearing of 45° as 045°?
Bearings conventionally use three figures, making the directional reading clear and consistent.
Build a scale drawing from distance and bearing
A complete scale drawing can turn a direction-and-distance problem into a measurable triangle. Each stated distance becomes a scaled length and each bearing becomes a correctly oriented ray.
Choose a scale that fits the page while leaving enough size for accurate measurement. Construct known information first, mark the desired segment or angle, then convert any measured length back into real units. The final result inherits the drawing’s measurement accuracy.
B is 6 km from A on a bearing of 060°. Draw it using 1 cm to represent 2 km.
- Convert 6 km to a drawing length of 3 cm.
- Mark A and draw its north line.
- Use a protractor to mark 60° clockwise from north.
- Use a ruler to measure 3 cm along that direction and mark B.
For a second leg, draw a fresh north line through B. Measure the required straight-line distance or bearing from your completed drawing, allowing for drawing accuracy.
Pause and explainWhy should the scale not make the entire drawing only a few millimetres wide?
Small drawing errors would become a large fraction of the measured length, making the converted answer unreliable.
Your turn. State the starting point.
Write the scale in usable units and draw north at every point that needs a bearing. Do not measure a bearing from whichever side happens to look convenient.
After finding a drawing length, show its conversion back to the real distance. Check that the result has a sensible size and direction in the original situation.
Convert 4.6 cm on a 1 : 50 000 map into kilometres.
Reveal worked answer
The bearing of P from Q is 312°. Find the bearing of Q from P.
Reveal worked answer
A point is due west of A. Give its bearing from A, and the reverse bearing.
Reveal worked answer
Using 1 cm to 5 m, what drawing length represents 37 m?