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Geometry, NAP-A3-CA32

Here is a map of Crikey Island.

The shortest distance from Point Nobby to Gilbos is 900 m.
 

 
The shortest distance from Point Nobby to Fire Beach is closest to

`text(1050 m)` `text(1900 m)` `text(2100 m)` `text(2450 m)`
 
 
 
 
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`text(2100 m)`

Show Worked Solution

`text(Let)\ w =\ text(grid width)`

`text(Distance from Point Nobby to Gilbos) =4.5w`

`:. 4.5 w` `= 900`
`w` `= 200\ text(metres)`

 

`:.\ text(Distance from Point Nobby to Fire Beach)`

`= 10.5 w`

`= 10.5 xx 200`

`= 2100\ text(metres)`

Geometry, NAP-D3-CA28 SA

On the map below, York is 60 km from Karkoo.

The town of Cootra is not shown on the map.

Cootra is due east of Barwell and due North of Ungarra.

What is the distance from Ungarra to Cootra?
 

   km
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`90`

Show Worked Solution

`text(4 grids between Karkoo and York)`

`=> 1\ text(grid interval)` `= 60/4`
  `= 15\ text(km)`

 

`:.\ text(Ungarra to Cootra)` `= 6\ text(grid intervals)`
  `= 6 xx 15`
  `= 90\ text(km)`

Geometry, NAP-E3-CA21

 
Peter is at the cafe of a theme park.

He leaves the cafe heading east on the pathway.

He makes a right turn and walks until he reaches a building.

In total, Peter walks 110 metres.

Which area of the park does Peter walk to?

`text(Ferris Wheel)` `text(Roller Coaster)` `text(Show Bags)` `text(Water World)`
 
 
 
 
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`text(Show Bags)`

Show Worked Solution

`text(S)text(ince the grid measures 20 m × 20 m, Peter)`

`text(will end up in the Show Bags area.)`

Geometry, NAP-F3-CA29 SA

Towns  `A, B and C` are marked on the scale diagram below.

The distance from Town  `A`  to Town  `B`  is 9 km.

What is the distance from Town  `B`  to Town  `C?`

   kilometres
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`3.6`

Show Worked Solution

`text(Let)\ \ d = text(distance of Town)\ B\ text(to Town)\ \ C`

`text(S)text(ince the diagram is a scale diagram,)`

`d/9` `= 2/5`
`:. d` `= (9 xx 2)/5`
  `= 3.6\ text(km)`

Geometry, NAP-H3-NC27 SA

Grant was making a scale drawing of a pipeline on grid paper.

The full length of the pipeline is drawn to scale on the grid below. It consists of 8 identical sections joined together (not shown on the diagram).
 

 
What is the length of each section of pipeline?

  metres
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`25`

Show Worked Solution
`text(S)text(ection length)` `= text(total length)/text(number of sections)`
  `= (5 xx 40)/8`
  `=200/8`
  `= 25\ text(metres)`

Geometry, NAP-H3-CA27 SA

Jana drew a diagram of her tennis racquet.
 

 
The actual length of her racquet is 60 centimetres.

What is the actual width of her racquet head?

   centimetres
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`26`

Show Worked Solution

`text(Racquet is 30 grid intervals long.)`

`text(30 intervals)` `= 60\ text(cm)`
`:. 1\ text(grid interval)` `= 2\ text(cm)`

 

`text(Racquet head is 13 grid intervals high,)`

`:.\ text(Head width)` `= 13 xx 2`
  `= 26\ text(cm)`

Geometry, NAP-H3-CA01

This is a street map.
 

 

 
About how far is it from Matt's house to Ali's house?

`40\ text(metres)` `100\ text(metres)` `160\ text(metres)` `200\ text(metres)`
 
 
 
 
Show Answers Only

`text(100 metres)`

Show Worked Solution

`text(The distance between Matt and Ali’s house is)`

`text(about 2.5 times the width of the scale interval)`

`text(that is equal to 40 metres.)`

`:.\ text(Distance)\ ~~ 2.5 xx 40 ~~ 100\ text(metres)`