LociA 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 1The 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 SheetPlace all of your Smarties so that they are the same distance away from points B and C.

B

C

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:

B

C

Locus 2The 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.

B

C

Locus of all points Equidistant from the points B and C.

Green SheetPlace your Smarties so that they are the same distance away from the lines X and Y.

X

Y

Green SheetWhen 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 3The Locus of all points equidistant from the Line X and the Line Y is an Angle Bisector.

Locus of all points equidistant from the Lines X and Y.

X

Y

Pink Sheet

Place your Smarties so that they are 6 cm away from the Line DE.

ED

Pink Sheet

When you placed your Skittles so that they were 6 cm away from the Line DE it should have looked like this:

ED

Locus 4The Locus of all Points 6 cm away from the Line DE is 2 semi-circles joined by 2 straight lines.

ED

Locus of all points 6 cm away from the Line DE.

Dark Yellow SheetPlace your Smarties so that they are 4 cm away from the Rectangle.

Dark Yellow SheetWhen you placed your Smarties so that they were 4 cm away from the Rectangle it should have looked like this:

Locus 5The 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 6The 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 SheetPlace your Smarties so that they are 4 cm away from the Shape.

Blue SheetWhen you placed your Smarties so that they were 4 cm away from the Shape it should have looked like this:

Locus 7The 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.