Scale Drawings (SQA National 5 Applications of Mathematics): Revision Note

Scale drawings

What is a scale?

• A scale refers to a ratio

  • This ratio describes the relationship between the drawn size and the real-life size

• Maps are usually drawn to a scale

• The ratio will work for any unit of length applied to both sides

• The scale can be given without units

  • e.g. 1 : 10,000 means 1 cm on the drawing is 10,000 cm in real life

• The scale can be given with different units

  • e.g. 1 cm : 100 m means 1 cm on the drawing is 100 m in real life

How do I measure or draw a line accurately?

• You need to have a ruler which uses millimetres

• Align 0 on the ruler with the starting point

• Make sure the ruler is in the required direction

• For measuring:

  • find where the endpoint meets the ruler

  • read off the number to the nearest millimetre

• For drawing:

  • draw a straight line using the ruler from 0 to the required measurement

How can I use a scale to find lengths for an accurate drawing?

• Questions normally ask you to draw a navigation course to scale

• STEP 1
  Divide the actual distance by the relevant part of the ratio

  • e.g. suppose the scale is 1 cm : 1.5 km and the actual distance between A and B is 5.4 km

    • the scale distance is 5.4 ÷ 1.5 = 3.6 cm

• STEP 2
  Measure this distance from the starting point

  • e.g. measure 3.6 cm from A in the direction that will be given

How can I use a scale to find the actual lengths from a map?

• Questions sometimes ask you to find the actual distance between two points using a map

• STEP 1
  Use a ruler to measure the distance accurately on the map

  • e.g. measuring a length from A to B as 5.8 cm

• STEP 2
  Use the scale to find the actual distance in the same units

  • e.g. suppose the scale is 1 cm : 1500 m

    • the actual distance = 5.8 × 1500 m = 8700 m