# Locus

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## Locus

A** locus** is simply a set of points that satisfy some sort of condition. Here are some common **loci **that you need to be able to draw...

The set of points, which are the same distance from a single point, is a **circle.**

* For example:* Use a pair of compasses. Draw the locus of points that is 5cm away from the cross marked.

The set of points that are the same distance from **two points** is a **perpendicular line** straight down the middle! You can draw this by finding the middle with your ruler then drawing a line at 90^{0} or you cantry this **clever way** just using compasses:

**1.** Set your compasses so that they are **roughly** the same as the distance between the points (or less if you don't have a lot of room!).

**2.** Put the point of the compasses on the first cross and do two arcs - one above the points and one below.

**3. ** Put the point on the second cross and do the same thing so that you cross the first arcs (making sure you keep the compasses the same distance apart).

**4.** Now simply draw a line straight down the middle through the points where the arcs cross.

* Note:* Don't rub the arcs out, so the examiners will be able to see what you've done!

**Click 'Show Me' below and the diagram will show you each step:**

When two lines meet, you get an **angle.** The set of points that are the same distance away from both lines is a straight line down the middle which **bisects** (cuts in half) the angle. Again, you could draw this line down the middle by using a protractor to measure the angle and halve it but, yes you've guessed it, there's a **clever way!**

**1.** Get a pair of compasses and place the point where the two lines meet. Draw little arcs that cross each of the lines.

**2.** Now, keeping the compasses set, put the point on each line where your arc has crossed it and draw another little arc in-between the two lines. You should now have another two little arcs in the middle.

**3.** Draw a straight line from the angle through the point where your little arcs cross and you've done it!

**Confused? Click 'Show Me' below and the diagram will show you each step:**