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You should already know:
- How to construct perpendicular lines using a ruler and set square.
- How to construct parallel lines using a ruler and set square.
You will learn:
- How to find the locus of a point equidistant from a fixed point.
- How to find the locus of a point equidistant from a line or line segment.
- Combine simple loci.
Locus & loci
The word 'locus' is Latin for 'place'. The plural is always 'loci' and never 'locuses' (unfortunately).
What is a locus?
In mathematics we usually mean one of two things when we talk about a locus:
1. The path traced out by a moving object.
2. All the points that satisfy some conditions.
Here the condition is 3cm from A. In formal language we would say:
The locus of points equidistant from a fixed point is a circle.
The Top Three Loci
We have seen one of the most common loci - the circle. Here are two more you will come across:
If we have the condition 5cm from a line then we get another locus.
The locus of points equidistant from a fixed line is two lines parallel to the fixed line.
Now we will look at a more complicated example - the locus of points equidistant from a line segment.
Exam Tip
Don't rub out your construction lines - they show how you got the locus. It's OK to go over the final locus in colour or with a heavier pencil stroke so it stands out better but make sure the construction lines can be seen.
The locus of points equidistant from a line segment is a 'running-track' or 'capsule' shape.
So...
Let's try to solve a problem:
Quick Test
Q. The ball is kicked off the block. What will the locus traced out by the ball look like?
Q. Which of these shows the locus of points 3cm from the black L-shape?
Next: Loci & Construction 2 >