Loci and constructing loci
A A path formed by a point which moves according to a rule. The plural form is loci. 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.
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 line AB. How would you draw an accurate diagram showing the flowerbed, using a scale of 1 cm:1 m?
Image caption, Draw a line parallel to AB 1 cm from AB. Shade in the area between this line and the line AB
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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.
To construct a locus around a point you will need to first construct the line and then shade the appropriate region given the question.
Question
A dog is on a lead measuring 3 m. The other end is attached to a post in the middle of a garden.
Using a scale of 1 cm = 1 m, shade the area the dog can reach.
Setting your compass to 3 cm, draw a circle with the post at the centre.
Shade the area inside the circle as this is the area the dog will be able to reach; anywhere outside this circle will be out of reach.