Loci and constructions

This goat is tethered
in the middle of a field.
What will the area of grass
he eats look like?

This puppy is chained to a rail, his chain can move along the rail.
What shape area
can he roam in?

A LOCUS is a path.
The path is formed by a point which moves according to some rule.
The plural of locus is loci.

Maths compass

For this task you may need:

Consider/think…
If
?m
?m
20m
30m

Online
http://www.echalk.co.uk/NGfL-Cymru/eng/Maths/loci/ism/lociISM.html

Symbols are marked

The property developer’s dilemma
15 minutes
End

Extra time
5 minutes

In each of the following cases construct an accurate diagram to show the area of grass that Gilbert can munch on.
Gilbert is a goat and he likes eating grass.
The farmer keeps him in a rectangular field measuring
10 metres by 8 metres.

If…
1cm represents 1m
2cm represents - ?m
6cm represents - ?m

1cm represents 1m
2cm represents - 2m
6cm represents - 6m
If…

Construct an accurate diagram

1) Gilbert is tethered to the corner of
the field by a 6 metre long rope.
Construct an accurate diagram
1cm represents 1m

2) Gilbert is tethered to the midpoint of the longer side of the field by a 7 metre long rope.
Construct an accurate diagram
1cm represents 1m

3) Gilbert is tethered to the shorter side of the field, 2 metres from the corner, by a 5 metre long rope.
Construct an accurate diagram
1cm represents 1m

4)Gilbert is tethered to the centre of the field by a 3 metre long rope.
Construct an accurate diagram
1cm represents 1m

5)The farmer mistakenly tethers Gilbert to the outside corner of the field using a 4.5 metre long rope.
Construct an accurate diagram
1cm represents 1m

6)The farmer mistakenly tethers Gilbert to the outside corner of the field using a 5 metre long rope.
Construct an accurate diagram
1cm represents 1m

7)The farmer tethers Gilbert outside the field, to a point 3 metres along from the corner on the longer side. The farmer uses a 5 metre long rope.
Try this one out – it’s an interesting solution!
1cm represents 1m

8)For some reason known only to him, the farmer fixes a 2 metre long pole along the centre of the field. Gilbert is tethered to this horizontal pole so that his
(2 metre long) rope can slide along. it.
Construct an accurate diagram
1cm represents 1m