math
posted by john on .
please help me I need to finish this so that I can go into grade 11. A new water tower must be equidistant from three communities. They are located at (25, 20) (5, 40) and (15, 30). Find the coordinates of the point where the water tower should be built which i am assuming is the circumcenter. Please give all steps

I will describe the method for you, but you must do the work.
Label the points A, B, and C
The centre of the circle will lie on the intersection of the right bisectors of AB and AC
1. Find the midpoint of AB
2. find the slope of AB
3. The slope of the rightbisector will be the negative reciprocal of the slope of AB
e.g. slope AB = (20+40)/(25 + 5) = 60/20 = 3
so the slope of the rightbisector is 1/3
You now have the slope of that line and a point on it, (its midpoint)
Find the equation of the line
repeat the above steps to get the rightbisector of AC
solve the two equations, the solution would be the position of the tower. 
hard