Step by step
The question
Question: construct the perpendicular bisector of a line A B, 9 cm long.
perpendicular bisector of AB = 9 cm
The perpendicular bisector cuts A B in half, at a right angle.
bisector = cuts in half; perpendicular = at 90°
1 Draw AB
Draw A B, 9 cm long.
2 Arcs from A
Open the compass to more than half of A B: 6 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.
Careful: keep the compass the same for both ends
3 Arcs from B
Keep the same opening.
From B, draw two arcs.
They cross the first arcs at P and Q.
4 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.
5 Check
Let's check: A M and M B are both 4.5 cm, and the angle at M is 90°.
So it is right!
AM = MB = 4.5 cm, angle at M = 90°
Let's look back.
First: draw AB.
Then: arcs from A.
Then: arcs from B.
Then: join the crossings.
Last: check.
Answer
perpendicular bisector of AB = 9 cm