C4.3 Scale drawings

Learning objectives

C4.3.1Draw and interpret scale drawings.• Draw and interpret scale drawings.C4.3.2Use and interpret three-figure bearings• Use and interpret three-figure bearings. A ruler must be used for all straight edges. Bearings are measured clockwise from north (000° to 360°). e.g. find the bearing of A from B if the bearing of B from A is 025°. Includes an understanding of the terms north, east, south and west. e.g. point D is due east of point C.

A scale drawing keeps every length in the same fixed ratio, so measurements on the drawing can be converted to actual lengths and actual lengths can be reduced to drawing lengths.

$\text{scale }1:n:\qquad \text{actual length}=n\times\text{drawing length}$

Put both lengths in the same unit before using a ratio. For a scale of $1:50\,000$ , $1$ cm on the drawing represents $50\,000$ cm $=0.5$ km in reality. A measured map length of $8.5$ cm therefore represents $8.5\times0.5=4.25$ km.

To draw a distance, reverse the conversion: drawing length $=$ actual length $\div n$ , after matching units. Rule straight edges. If a point is fixed by its distances from two known points, convert both distances and use two arcs; their intersection locates the point.

A useful scale must fit the available page while remaining large enough to measure accurately. A route of $10.8$ km at $1:500\,000$ is only $2.16$ cm long, so that scale may be too small for a detailed drawing.

The factor $n$ applies to lengths, not directly to areas. At scale $1:n$ , areas change by $n^2$ . Never mix centimetres and metres or kilometres inside the same ratio.

A bearing is the clockwise angle from north at the starting point, written with three figures from $000^\circ$ to $360^\circ$ .

Direction	Bearing
north	$000^\circ$
east	$090^\circ$
south	$180^\circ$
west	$270^\circ$

For the bearing of $B$ from $A$ , place north at $A$ , centre the protractor at $A$ , and measure clockwise from the north line to $AB$ . To draw a bearing, mark that clockwise angle from north, rule the ray, then use the stated scale to mark the distance.

$\text{reverse bearing}=\begin{cases}b+180^\circ,&b<180^\circ\\b-180^\circ,&b\ge180^\circ\end{cases}$

If the bearing of $B$ from $A$ is $025^\circ$ , the bearing of $A$ from $B$ is $025^\circ+180^\circ=205^\circ$ . If the original bearing is $322^\circ$ , the reverse is $322^\circ-180^\circ=142^\circ$ .

The phrase “of $B$ from $A$ ” means start at $A$ , not at $B$ . Write leading zeros: $65^\circ$ is the three-figure bearing $065^\circ$ . Measure clockwise even when the shorter turn is anticlockwise.

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—C4.4 SimilarityRead

C4.3 Scale drawings

Learning objectives

Convert and construct scale drawings

Measure, draw and reverse three-figure bearings

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