Constructions and Loci : Higher
Which grade are you…..?
1
6 cm
6 cm
7 cm
6 cm
Grade D
Use a ruler and compasses to construct the rhombus shown below.
6 cm
2
Grade C
The diagram shows a plan of a garden. A gnome is to be placed in the garden such that it
is less than 10 m from C and is an equidistant from AB and BC.
Using a scale of 1cm to 1m draw a plan and show all of the possible positions of the
gnome
B
C
9m
A
12 m
3
A man wants to build a house within the triangle. The house needs to be at least 90m
from each of the telegraph poles. The floor plan of the house shows that it will measure
50m by 70m.
Grade C/B
Telegraph poles A, B and C are on the corners of an isosceles triangle such that AB = AC =
200m and BC = 250m.
Is there room for the house in the field?
Show how you decide.
4
Alex is sitting directly in front of the TV, 4m away from it. Cathy is 3.5 m from the TV to
the right of Alex. Alex and Cathy are sitting 2.5 m apart.
The distance between Alex and Ben is the same as the distance between Alex and Cathy.
Ben is 3m from the TV and is sitting to the left of Alex.
Draw an accurate plan of the room showing the position of Alex, Ben and Cathy.
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Grade B
Three friends Alex, Ben and Cathy are sitting watching a DVD.
Constructions and Loci : Higher
Which grade are you…..?
1
Use a ruler and compasses to construct the rhombus shown below.
6 cm
Check by measuring


Grade D
6 cm

7 cm
106° - 110°

6 cm
6 cm
2
rectangle measuring 9 cm by 12 cm
cmcmcm
arc radius 10 cm
angle bisector at B
correct part highlighted
9m
A
12 m
Grade C
The diagram shows a plan of a garden. A gnome is to be placed in the garden such that it
is less than 10 m from C and is an equidistant from AB and BC.
Using a scale of 1cm to 1m draw a plan and show all of the possible positions of the
gnome
B
C
3 Telegraph poles A, B and C are on the corners of an isosceles triangle such that AB = AC =
A man wants to build a house within the triangle. The house needs to be at least 90m
from each of the telegraph poles. The floor plan of the house shows that it will measure
50m by 70m.
Is there room for the house in the field?
Show how you decide.
Three friends Alex, Ben and Cathy are sitting watching a DVD.Alex is sitting directly in front of the TV, 4m away from it.
Cathy is 3.5 m from the TV to the right of Alex. Alex and Cathy are sitting 2.5 m apart.The distance between Alex and
Ben is the same as the distance between Alex and Cathy.Ben is 3m from the TV and is sitting to the left of Alex.
3 semi-circles centred on TV – suitable scale
arc centred on ‘Alex’ – correct radius (2.5m)
TV
B
C
3 points correctly marked and labelled
A
www.mathsbox.org.uk
15 Marks
Grade B
4
YES
scale drawing of the triangle
3 arcs drawn accurately
house drawn to scale
Grade C/B
200m and BC = 250m.