Scale drawings Revision Notes

A scale drawing is a representation of an object or area where all lengths are proportionally reduced or enlarged according to a fixed ratio called the scale. This allows large objects or distances to be shown on a manageable size of paper while preserving accurate shape and relative dimensions.

For example, a scale of 1:100 means that 1 cm on the drawing represents 100 cm (or 1 m) in reality. To create a scale drawing, you measure actual lengths and then convert them using the scale factor before drawing them with a ruler.

Using a ruler ensures that straight lines are drawn accurately to the required length, which is essential for maintaining the correct proportions in the drawing.

• Scale drawings preserve the shape and proportions of the original object.
• The scale is a ratio comparing drawing length to actual length.
• A ruler is used to draw straight lines to the scaled lengths.

To construct a scale drawing: first, identify the scale ratio (e.g., 1:50, 1:200). Then, measure the actual lengths of the object or distances between points.

Next, convert these actual lengths to the drawing lengths by dividing by the scale factor. For example, if the actual length is 300 cm and the scale is 1:100, the drawing length is 300 ÷ 100 = 3 cm.

Use a ruler to draw straight lines of these calculated lengths, ensuring accuracy by aligning the ruler carefully and marking points precisely. Repeat this for all sides or segments to complete the drawing.

• Identify the scale ratio before starting.
• Convert actual lengths to drawing lengths by dividing by the scale factor.
• Use a ruler to draw straight lines of the calculated lengths.
• Check measurements carefully to avoid errors.

Bearings are angles used to describe direction, measured clockwise from the north line. Bearings are always given as three-figure numbers from 000° to 360°, where 000° or 360° represents north, 090° east, 180° south, and 270° west.

For example, a bearing of 025° means the direction is 25 degrees clockwise from north towards east.

Bearings help specify the direction from one point to another precisely, which is useful in navigation and map reading.

• Bearings are measured clockwise from north (000° to 360°).
• Always express bearings as three figures (e.g., 025°, 090°, 180°).
• Cardinal directions correspond to bearings: North = 000°, East = 090°, South = 180°, West = 270°.

If you know the bearing of point B from point A, you can find the bearing of point A from point B by adding or subtracting 180°, because the two bearings are in opposite directions.

For example, if the bearing of B from A is 025°, then the bearing of A from B is 025° + 180° = 205°. If the sum exceeds 360°, subtract 360° to keep the bearing within 000° to 360°.

This calculation assumes bearings are measured clockwise from north and that the points are distinct.

• Opposite bearings differ by 180°.
• Add 180° to the given bearing to find the reverse bearing.
• If the result is greater than 360°, subtract 360° to get a valid bearing.
• Example: Bearing of B from A = 025°, bearing of A from B = 205°.

Cardinal directions (north, east, south, west) are fundamental for describing the relative positions of points on a scale drawing or map.

For example, if point D is directly east of point C, then the bearing of D from C is 090°. Similarly, if a point lies directly south of another, the bearing is 180°.

Understanding these directions helps interpret bearings and locate points accurately on drawings or maps.

• North corresponds to 000°, east to 090°, south to 180°, and west to 270° bearings.
• Points directly east or west lie on a horizontal line; points directly north or south lie on a vertical line.
• Use cardinal directions to check or describe bearings and relative positions.