Step by step
The question
Question: draw the locus of the points that are the same distance from A and from B, with A B = 5 cm.
A locus is the set of all the points that follow a rule.
Here: the same distance from A as from B.
1 Draw AB
Draw A B, 5 cm long.
2 Try some points
The middle of A B is the same distance from both.
So is a point straight above the middle.
They all lie on one line.
3 Arcs from A
Open the compass to more than half of A B: 3.5 cm.
From A, draw an arc above and an arc below.
Careful!
Do not change the compass.
The arcs from B must have the same opening as the arcs from A.
4 Arcs from B
Keep the same opening.
From B, draw two arcs.
They cross the first arcs at P and Q.
5 Join the crossings
With a ruler, join P and Q.
This line cuts A B in half at M, at a right angle: the perpendicular bisector.
6 Check
Let's check: A M and M B are both 2.5 cm, and the angle at M is 90°.
So it is right!
Let's look back.
First: draw AB.
Then: try some points.
Then: arcs from A.
Then: arcs from B.
Then: join the crossings.
Last: check.