Loci and constructions
Loci are a set of points with the same property. Loci can be used to accurately construct lines and shapes. Bearings are three figure angles measured clockwise from North.
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 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?
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.
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?
- 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?
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.