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.
Light Yellow Sheet
Place all of your Smarties so that they are 8 cm
away from the point A.
A
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:
A
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.
A
Locus of all
points 8 cm
away from
the point A.
Lilac Sheet
Place all of your Smarties so that they are the same
distance away from points B and C.
C
B
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:
C
B
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.
C
B
Locus of all
points
Equidistant
from the points
B and C.
Green Sheet
Place your Smarties so that they are the same distance
away from the lines X and Y.
X
Y
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
Locus 3
The Locus of all points equidistant from the Line X
and the Line Y is an Angle Bisector.
X
Y
Locus of all
points
equidistant
from the
Lines X and Y.
Pink Sheet
Place your Smarties so that they are 6 cm away from
the Line DE.
D
E
Pink Sheet
When you placed your Skittles so that they were 6 cm
away from the Line DE it should have looked like this:
D
E
Locus 4
The Locus of all Points 6 cm away from the Line DE is 2
semi-circles joined by 2 straight lines.
D
E
Locus of all
points 6 cm
away from
the Line DE.
Dark Yellow Sheet
Place your Smarties so that they are 4 cm away from
the Rectangle.
Dark Yellow Sheet
When you placed your Smarties so that they were 4 cm
away from the Rectangle it should have looked like
this:
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.
Red Sheet
Place your Smarties so that they are 4 cm away from
the Shape.
Red Sheet
When you placed your Smarties so that they were 4 cm
away from the Shape it should have looked like this:
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.
Blue Sheet
Place your Smarties so that they are 4 cm away from
the Shape.
Blue Sheet
When you placed your Smarties so that they were 4 cm
away from the Shape it should have looked like this:
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.
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.
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.