E4.3 Scale drawings

Learning objectives

E4.3.1Draw and interpret scale drawings.• Draw and interpret scale drawings.E4.3.2Use 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 preserves every length in one constant ratio, so measured drawing lengths can be converted to real lengths and real lengths can be converted back for accurate drawing.

\text{scale factor}=\frac{\text{drawing length}}{\text{actual length}}

Convert drawing and actual measurements to the same unit.
Write the scale as a ratio or statement, such as $1:40\,000$ or $1$ cm represents $400$ m.
To interpret the drawing, multiply by the actual length represented by one drawing unit. To draw, divide the actual length by that value.
Use a ruler for every straight edge and label the final real-world unit.

At a scale of $1:40\,000$ , $1$ cm on the map represents $40\,000$ cm $=400$ m $=0.4$ km. A map length of $7.5$ cm therefore represents $7.5\times0.4=3$ km; a real distance of $5$ km would be drawn as $5\div0.4=12.5$ cm.

A length scale does not apply unchanged to area. If lengths use scale factor $k$ , corresponding areas use $k^2$ . Always convert square units before taking a square root to recover a length scale from two areas.

The bearing of $B$ from $A$ is the clockwise angle at $A$ , starting from the north line at $A$ and ending at the direction from $A$ to $B$ .

Start at the point named after ‘from’ and draw or identify north there.
Turn clockwise from north to the destination line.
Measure or calculate the angle from $000^\circ$ to $360^\circ$ .
Write exactly three figures: for example $025^\circ$ , $090^\circ$ or $247^\circ$ .

The cardinal bearings are north $000^\circ$ , east $090^\circ$ , south $180^\circ$ and west $270^\circ$ . A ruler must be used for every straight direction line.

Reverse bearings differ by $180^\circ$ . If the bearing of $B$ from $A$ is $025^\circ$ , the bearing of $A$ from $B$ is $025^\circ+180^\circ=205^\circ$ . If adding $180^\circ$ passes $360^\circ$ , subtract $180^\circ$ instead.

The words ‘of’ and ‘from’ fix different points: the bearing of $B$ from $A$ is measured at $A$ , not at $B$ . Bearings are always clockwise from north, even when the shorter visible angle is anticlockwise.

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—E4.4 SimilarityRead

E4.3 Scale drawings

Learning objectives

Draw and read from scale

Use three-figure bearings

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