Geometrical Construction and Scales
What the exam tests
This domain tests accurate construction of perpendiculars, angle bisectors, parallels, regular polygons, tangents, conic curves and engineering scales. Scale questions usually ask for a plain or diagonal scale from a representative fraction (RF), with correct subdivision and labelling.
Core rules
- RF = drawing length ÷ actual length, with both lengths in the same unit. A scale must be long enough for the maximum length but not excessively long.
- Plain scale: divide the length into major units and subdivide the first major unit. Diagonal scale: use a rectangle whose height is divided into equal parts; diagonals give the second subdivision.
- Construct polygons by exact geometry, not by guessing angles: use a circle, chord lengths, or bisection as required.
- For a diagonal scale, the diagonal is drawn from the zero of the subdivided first unit to the top of the last division; horizontal lines from the diagonal give the small readings.
Worked example
Construct a plain scale with RF 1:50 to read metres and decimetres up to 8 m. Scale length = 8 m ÷ 50 = 0.16 m = 160 mm. Draw a 160 mm line and divide it into 8 equal parts of 20 mm; each represents 1 m. Subdivide the first part into 10 equal parts of 2 mm; each represents 0.1 m. Mark 0 at the first major division, numbers 1–7 to the right, and decimetres 1–10 to the left.
Traps
Using different units in the RF calculation is the main numerical error. Do not mark the zero at the left end; it belongs at the junction of the major and subdivided parts. Diagonal scales need a completed rectangle, not just slanted lines. Label the scale with its RF and units.