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Perpendicular Bisectors and Circumcenters

I'm really stuck on step number one. I know how to find the midpoint of a segment, but the problem does not give me the actual points to plug into the midpoint formula, and I'm lost as to how to find them. Do I use the ruler to find the points? Or should I draw a coordinate plane on a separate piece of paper, trace the triangle on it, then find the points?

Here is my problem:

Attachment 29299

The thing is if I draw a coordinate plane and trace the triangle, how will I know which quadrant the triangle will go in? And if I use the ruler method, how will that give me my points? The rest of the steps are simple; they are just asking me to fold the paper and draw the perpendicular lines. It is just step one (finding the points to plug into the midpoint formula) that I am having a difficult time with . I would really appreciate it if someone showed me how to do step one.

Re: Perpendicular Bisectors and Circumcenters

Hey drzombie123.

For this exercise its not computational: you need to use the physical piece of paper to get the mid-point. I haven't done this kinld of thing for a very long time, but if you have a ruler, then you can find the midpoint by placing the ruler along a specific line (HK for example is the line formed from drawing a straight line from point H to point K) and then finding the point where it divides the line into equal lengths.

If you have learned how to do this with a compass then you will want to use this to check your work.

So as an example: if you put your ruler against the line HK and you find its say 4 inches, then the mid-point will be 2 inches along that same line from either points H or K.

Re: Perpendicular Bisectors and Circumcenters

You can draw the perpendicular bisector of a line segment using a compass and scale. let us say that we have to draw perpendicular bisector of a line segment AB.

step 1. With A as center and radius greater than half of AB draw an arc n either side of line segment AB.

Step 2. with B as center and the same radius ( that is the radius taken in step 1 ) draw arcs on either side of AB intersecting the arcs drawn in step 1 at P and Q.

Step 3. join PQ intersecting AB at M.

PQ is the perpendicular bisector of AB and and L is the mid point of AB.

Also please note that the circum-center lies inside the triangle for acute angle triangle, on the triangle for right angle triangle ( it lies on hypotenuse ) and outside an obtuse angle triangle.