Loci

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

Running track with locus path highlighted

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.

Clock face with locus path highlighted
curriculum-key-fact
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

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?

Path of cow highlighted

The locus is a circle 4 m from the post.

Cow following a locus path with a radius of 4m

Locus from a line

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

Example

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?

Empty flower bed

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

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?

Zoo enclosure (DEFG)

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.

Zoo enclosure (DEFG) with 2m surrounding locus highlighted

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.

Area created by locus, shaded blue