Scale drawings/maps | Year 9

01 / LEARN

Understand the idea.

Read both sides in the same unit

A scale of $1 : 50 000$ compares drawing and actual lengths in the same unit. One centimetre represents $50 000 cm = 500 m = 0.5 km$ . The scale denominator does not name a new unit.

To go from map to reality, multiply a length by the denominator, then convert units. To go from reality to the drawing, first express the actual length in the drawing unit, then divide by the denominator.

Follow the route that is asked for

Follow the distance named in the question. A route through several points adds its separate legs; a straight-line distance joins the endpoints directly. On a grid, count spaces between grid lines, because these spaces represent the measured intervals.

A written ratio assumes the map is at its intended size. Enlarging or shrinking the printed map changes that ratio. A scale bar resizes with the map, so it can still compare distances on the resized copy.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Map to real distance

On a $1 : 25 000$ map, a path is 7.2 cm long. Find its real length in kilometres.

Worked solution

1
Interpret the scale in centimetres.
$1 cm 25 000 cm$
One map centimetre corresponds to twenty-five thousand actual centimetres; both terms use the same unit.
2
Find the actual path length in centimetres.
$L = 7.2 \times 25 000 = 180 000 cm$
Every centimetre of the measured path represents the same actual distance.
3
Convert to kilometres.
$L = \frac{180 000}{100 000} = 1.8 km$
One kilometre contains one hundred thousand centimetres.

Answer

1.8 km

EXAMPLE 02

Choose the route

Using the map, find the length of the route A–B–C.

Worked solution

1
Measure each specified leg on the grid.
$A B = 6 cm, B C = 4 cm$
The route follows six horizontal intervals and then four vertical intervals.
2
Add the two map lengths.
$L_{map} = 6 + 4 = 10 cm$
The route passes through B, so both legs must be included.
3
Convert one map centimetre to kilometres.
$50 000 cm = 0.5 km$
This map uses a scale of one to fifty thousand.
4
Scale the whole route.
$L_{actual} = 10 \times 0.5 = 5 km$
The same scale applies along both legs of the path.

Answer

5 km

03 / YOUR TURN

Try it yourself.

Check your understanding

A 9 m room is drawn using scale $1 : 100$ . How long is it on the drawing?

Show answer & reasoning

9 cm

Express the room length in centimetres: $9 m = 900 cm$ . The drawing is one hundredth of the actual length, so it measures $\frac{900}{100} = 9 cm$ .

Keep practising

6 worksheet questions · 13 marks

Open worksheet Worked solutions

Read the questions online

State what 1 cm represents on a $1 : 20 000$ map, in metres.
2 marks
A distance is 4.8 cm on a $1 : 50 000$ map. Find its actual length.
2 marks
Drawn at $1 : 200$ , what length represents a 14 m wall?
2 marks
A model is 18 cm long and represents a 9 m vehicle. Find the scale.
2 marks
On the supplied map, find only the actual distance A–B.
2 marks
A plan marked $1 : 100$ is enlarged so every printed length doubles. What is its new scale?
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

State what 1 cm represents on a $1 : 20 000$ map, in metres.
2 marks
$20 000$ cm $= 200$ m.
$200$ m
A distance is 4.8 cm on a $1 : 50 000$ map. Find its actual length.
2 marks
$4.8 \times 50 000 = 240 000$ cm $= 2.4$ km.
$2.4$ km
Drawn at $1 : 200$ , what length represents a 14 m wall?
2 marks
$14$ m $= 1 400$ cm.
$1 400 \div 200 = 7$ cm.
$7$ cm
A model is 18 cm long and represents a 9 m vehicle. Find the scale.
2 marks
$9$ m $= 900$ cm.
Scale $18 : 900 = 1 : 50$ .
$1 : 50$
On the supplied map, find only the actual distance A–B.
2 marks
A–B is six 1 cm squares.
$6 \times 0.5 = 3$ km.
$3$ km
A plan marked $1 : 100$ is enlarged so every printed length doubles. What is its new scale?
3 marks
An original 1 cm now becomes 2 cm but still represents 100 cm.
New scale $2 : 100 = 1 : 50$ .
$1 : 50$

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 9 proportional modelling, rates, scale, similarity and enlargement. Assumptions, interpretation and model limitations are taught alongside calculation.

Official curriculum source ↗

In this lesson

Understand the idea.

Read both sides in the same unit

Follow the route that is asked for

See the method in action.

Map to real distance

Interpret the scale in centimetres.

Find the actual path length in centimetres.

Convert to kilometres.

Choose the route

Measure each specified leg on the grid.

Add the two map lengths.

Convert one map centimetre to kilometres.

Scale the whole route.

Try it yourself.

Check your understanding

Keep practising