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What are the coordinates of the circumcenter of a triangle with vertices A(−1, 1) , B(5, 1) , and C(−1, −1) ?

AngelRay  Nov 4, 2017

Best Answer 

 #1
avatar+1375 
+3

The circumcenter of a triangle, in this case \(\triangle ABC\) is a point equidistant from the vertices of the triangle. This point also happens to be the the center wherein all the vertices are circumscribed about this particular polygon. Here's a diagram to clear up any confusion.

 

 

\(O\), the intersection of all three perpendicular bisectors, is the circumcenter. This point is also the center of the circle outlined in red. Now that you know this, let's actually find this mysterious point!

 

1. Graph the Triangle.

 

 

2. Find Equation for Perpendicular Bisector of 2 Sides

 

Since two sides of this triangle lie directly straight on the graph, use it to find the equation of the line. 

 

 

3. Find the Intersection of the 2 lines!

 

If you refer back to the previous graph, the intersection is at (2,0), which is the point of the circumcenter.

TheXSquaredFactor  Nov 5, 2017
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1+0 Answers

 #1
avatar+1375 
+3
Best Answer

The circumcenter of a triangle, in this case \(\triangle ABC\) is a point equidistant from the vertices of the triangle. This point also happens to be the the center wherein all the vertices are circumscribed about this particular polygon. Here's a diagram to clear up any confusion.

 

 

\(O\), the intersection of all three perpendicular bisectors, is the circumcenter. This point is also the center of the circle outlined in red. Now that you know this, let's actually find this mysterious point!

 

1. Graph the Triangle.

 

 

2. Find Equation for Perpendicular Bisector of 2 Sides

 

Since two sides of this triangle lie directly straight on the graph, use it to find the equation of the line. 

 

 

3. Find the Intersection of the 2 lines!

 

If you refer back to the previous graph, the intersection is at (2,0), which is the point of the circumcenter.

TheXSquaredFactor  Nov 5, 2017

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