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Maps and plans

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Position and transformation

Maps and plans

A map is a drawing of somewhere far too big to draw actual size. The scale is the deal you strike: this much on paper stands for that much in real life.

Scale: 1 cm represents 5 m12 cmon the drawing60 min real lifeƗ 5 Ā ā†’ real lifeĆ· 5 Ā ā†’ drawingWritten as a ratio, both numbers need the same unit:1 cm : 5 m Ā =Ā  1 : 500
Real life is bigger, so multiply going that way.

Three ways to write a scale

A SCALE DRAWING represents a real object. The SCALE links lengths on the drawing to lengths in real life. You can write it three ways: ā€¢ with 'represents' ā€” 1 cm represents 100 cm ā€¢ with 'to' ā€” 1 to 100 ā€¢ with a ratio sign ā€” 1 : 100 With 'to' or a ratio sign, both numbers must be in the SAME units. So '1 cm represents 10 m' has to be written 1 : 1000, because 10 m is 1000 cm.

Which way round?

Only two rules, and they are opposites: ā€¢ Drawing ā†’ real life: MULTIPLY by the scale. ā€¢ Real life ā†’ drawing: DIVIDE by the scale. Real life is always the bigger number, so if your answer came out smaller than the drawing, you divided when you should have multiplied.

Working with a map scale

A map has a scale of 1 : 50 000, and two villages are 8 cm apart on it. 8 Ɨ 50 000 = 400 000 cm That is a real distance, but nobody measures villages in centimetres. Convert: 400 000 cm Ć· 100 = 4000 m 4000 m Ć· 1000 = 4 km So the villages are 4 km apart.

Going the other way

The same map, and two towns 18 km apart in real life. How far apart on the map? Convert to the map's units first: 18 km = 18 000 m = 1 800 000 cm Then divide by the scale: 1 800 000 Ć· 50 000 = 36 cm Convert first, divide second. Doing it the other way round is where the mistakes happen.

Worked examples

1 cm represents 5 m; the drawing is 12 cm long

  1. Drawing to real life, so multiply.
  2. 12 Ɨ 5 = 60.

Answer: 60 m

The same scale; the building is 120 m tall

  1. Real life to drawing, so divide.
  2. 120 Ć· 5 = 24.

Answer: 24 cm on the drawing

1 : 50 000; villages 8 cm apart on the map

  1. 8 Ɨ 50 000 = 400 000 cm.
  2. 400 000 Ć· 100 = 4000 m.
  3. 4000 Ć· 1000 = 4 km.

Answer: 4 km

1 : 50 000; towns 18 km apart in real life

  1. 18 km = 18 000 m = 1 800 000 cm.
  2. 1 800 000 Ć· 50 000 = 36.

Answer: 36 cm on the map

Writing '1 cm represents 10 m' as a ratio

  1. Both numbers must use the same unit.
  2. 10 m = 1000 cm.

Answer: 1 : 1000

A plan at 1 : 20; a room 4 cm wide on the plan

  1. Plan to real life, so multiply.
  2. 4 Ɨ 20 = 80 cm.

Answer: 80 cm

Where you see this in real life

  • Every walking map has a scale bar. Without it you could not tell a two-hour hike from a ten-minute stroll.
  • Architects draw whole buildings at 1 : 100 so the plan fits on a desk and every measurement still works.

Key words

Scale drawing
a drawing that represents a real object
Scale
how lengths on a drawing relate to real lengths
Represents
stands for ā€” 1 cm represents 5 m
Plan
a scale drawing seen from above
Convert
change a measurement into different units
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