Coordinate geometry question

[okay]

I have a problem which goes like this:

"The vertices of triangle ABC are A(-3,3), B(3,2), and C(1,-4). Find the coordinates of the circumcenter."

Since it is asking for the point of intersection of the perpendicular bisectors of the triangle, the first thing I do is find the midpoint of points A and B, which is (0,2.5). Since the line I am looking for is perpendicular to line AB, I find the slope of AB, which is -1/6. So therefor a line perpendicular to it must have a slope of 6. So the perpendicular bisector of AB intersects AB at (0,2.5) and has a slope of 6. Putting that information into the point-slope equation, I get (y-2.5)=6(x-0), which when solved for y yields y=6x+2.5.

I repeat this process with line BC. The midpoint of BC is (2,-1), and its slope is 3. Putting that information into the point-slope form equation and solving for y, I get y=3x-7. If I have even been approaching the problem correctly thus far, I am still at a point now where I don't know what I'm supposed to do. I have the equations of the perpendicular bisectors as well as the point at which they bisect the sides, but I don't see what to do with this.

 

[Deleted member 4993]

I have a problem which goes like this:

"The vertices of triangle ABC are A(-3,3), B(3,2), and C(1,-4). Find the coordinates of the circumcenter."

Since it is asking for the point of intersection of the perpendicular bisectors of the sides of the triangle, the first thing I do is find the midpoint of points A and B, which is (0,2.5). Since the line I am looking for is perpendicular to line AB, I find the slope of AB, which is -1/6. So therefor a line perpendicular to it must have a slope of 6. So the perpendicular bisector of AB intersects AB at (0,2.5) and has a slope of 6. Putting that information into the point-slope equation, I get (y-2.5)=6(x-0), which when solved for y yields y=6x+2.5.

I repeat this process with line BC. The midpoint of BC is (2,-1), and its slope is 3. Putting that information into the point-slope form equation and solving for y, I get y=3x-7. If I have even been approaching the problem correctly thus far, I am still at a point now where I don't know what I'm supposed to do. I have the equations of the perpendicular bisectors as well as the point at which they bisect the sides, but I don't see what to do with this.

The circumcenter is the point where those bisectors [(y = 6x + 2.5) and (y= 3x-7)] intersect each other.

 

[Quaid]

at a point now where I don't know what I'm supposed to do

President Lincoln said, "Things which are equal to the same things are equal to each other. That's a rule of mathematical reasoning and its true because it works".

You have two expressions that equal the same thing: y

That is, the expression 6x + 2.5 equals y and the expression 3x - 7 equals y

Therefore, 6x + 2.5 equals 3x - 7 for some value x.

Solve this equation for x, and you will have the x-coordinate of the circumcenter. Once you know the x-coordinate, calculate the y-coordinate by substitution in 3x-7.

Please show your work, if you need more help.