Loci

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Loci
A Locus is any set of points which follow a
pattern or rule. You will now meet some of the
most common Loci (that means more than one Locus)
in the following activities.
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Light Yellow Sheet
Place all of your Smarties so that they are 8 cm
away from the point A.
A
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Light Yellow Sheet
When you placed your Smarties so that they were 8
cm away from the point A it should have looked
like this
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Locus 1
The Locus of all points 8 cm away from the point
A is a Circle with centre at A and a radius of 8
cm.
Locus of all points 8 cm away from the point A.
A
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Lilac Sheet
Place all of your Smarties so that they are the
same distance away from points B and C.
C
B
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Lilac Sheet
When you placed your Smarties so that they were
the same distance away from points B and C it
should have looked like this
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Locus 2
The Locus of all points the same distance away
from points B and C is a straight line which is
at a 90º to the line BC. It is called a
Perpendicular Bisector.
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Green Sheet
Place your Smarties so that they are the same
distance away from the lines X and Y.
X
Y
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Green Sheet
When you placed your Smarties so that they were
the same distance away from the lines X and Y it
should have looked like this
X
Y
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Locus 3
The Locus of all points equidistant from the Line
X and the Line Y is an Angle Bisector.
X
Locus of all points equidistant from the Lines X
and Y.
Y
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Pink Sheet
Place your Smarties so that they are 6 cm away
from the Line DE.
E
D
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Pink Sheet
When you placed your Skittles so that they were 6
cm away from the Line DE it should have looked
like this
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Locus 4
The Locus of all Points 6 cm away from the Line
DE is 2 semi-circles joined by 2 straight lines.
Locus of all points 6 cm away from the Line DE.
E
D
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Dark Yellow Sheet
Place your Smarties so that they are 4 cm away
from the Rectangle.
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Dark Yellow Sheet
When you placed your Smarties so that they were 4
cm away from the Rectangle it should have looked
like this
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Locus 5
The Locus of all Points 4 cm away from the
Rectangle is 4 quarter-circles joined by 4
straight lines.
Locus of all points 4 cm away from the Yellow
Rectangle.
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Red Sheet
Place your Smarties so that they are 4 cm away
from the Shape.
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Red Sheet
When you placed your Smarties so that they were 4
cm away from the Shape it should have looked like
this
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Locus 6
The Locus of all Points 4 cm away from the Shape
is a combination of quarter-circles, straight
lines and a right angle.
Locus of all points 4 cm away from the Orange
Shape.
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Blue Sheet
Place your Smarties so that they are 4 cm away
from the Shape.
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Blue Sheet
When you placed your Smarties so that they were 4
cm away from the Shape it should have looked like
this
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Locus 7
The Locus of all Points 4 cm away from the Shape
is again a combination of quarter-circles,
straight lines and right angles.
Locus of all points 4 cm away from the Blue Shape.
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Summary
For an Internal Corner the Locus of all points a
set distance away maps out a right angle.
For an External Corner the Locus of all points a
set distance away maps out a quarter-circle and 2
parallel lines.
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A goat is tied to a rope 5m long at the corner of
a building in a fenced field. Show the region of
grass that the goat can eat.
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