### 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.

## 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 >