# Perpendicular bisector

Sometimes we need to find the midpoint of a line, and other times we will need to draw a perpendicular line, and yet other times we will need to do both! This method does all of these with just a ruler and compass.

Above is our line segment.
Before we start using a compass, we need to set the radius for it. Select "Segment" from the line drop down menu.
We need our radius to be larger than half of the distance AB. Click in two empty spaces that are at least that distance apart. If you make a mistake you can undo or restart by clicking the button.
Now we are ready to draw! Choose the "Compass" tool from the compass drop down menu.
Click on your new line segment to set the radius. Then click on A or B. Geogebra will draw a circle of your chosen radius around the centre point A or B.
Do the same with a circle around the other of A and B and look where they intersect.

Imagine a line connecting points E and F in the applet above. How far along segment AB does the line EF cross it?
Try moving the points C and D in the applet above to change the radius. Do you think they will cross at the same place if you used a different radius?
Why was it important to have the radius be at least half of AB?
Finally, choose "Line" from the line drop down menu and connect your E and F together by clicking them.
On paper this is the same as joining them with a ruler and pencil, and congratulations on constructing a perpendicular bisector!

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