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. 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 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. B C 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. 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 4 The 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 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.