### 1) Loci

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

The runner is following a path. This path is a locus.

##### Locus around a point

The hands of a clock move around the clock and create a locus. The tip of each hand is always the same distance – **equidistant** – from the centre of the clock.

The locus the hands create is a circle.

**A locus of points at equal distance around a point is a circle.**

A pair of compasses must be used to create a locus around a point.

##### Question 1

Farmer Smith has tied a cow around a post on a rope 4 m long. What the locus of the cow as it moves around the post?

**Answer**: The locus is a circle 4 m from the post.

##### Locus from a line

A locus does not have to be a line – it can also be an area.

A flowerbed runs along the grass between A and B. The edge of the flowerbed is 1 m from the grass. How would you draw an accurate diagram showing the flowerbed, using a scale of 1 cm:1 m?

Draw a line parallel to AB 1 cm from AB. Shade in the area between this line and the line AB.

The edge of the flowerbed is the locus from the line AB, because it is at a set distance from the line.

##### Question

Visitors must stand at least 2 m away from the walls of the monkey enclosure at the zoo. How would you draw an accurate diagram to show where the visitors must not stand, using a scale of 1 cm:1 m?

**Answer**: Draw four lines parallel to each side of the rectangle, 2 cm away. Use a compass to draw rounded corners at D, E, F and G.

The straight line of the locus is parallel to the edges of the rectangle, because they are at a set distance from the edges. At each corner the locus is a quarter circle drawn from the fixed points D, E, F and G.

Visitors must not stand in the area between the rectangles. Shade this in.