1. what are the coordinates of the circumcenter of a triangle with vertices a(0,1), b(2, 1) , and c(2, 5) ? 2. what are the coordinates of the centroid of a triangle with vertices a(−6,  0) , b(−4,  4) , and c(0,  2) ?

We know that a circumcenter is the intersection of all three perpendicular bisectors of a triangle, which divides the sides equally. So, basically, we need to find a points which is equidistant from its ends of the side.

So, for points and , we have

, you can observe that we just replace the coordinates in an expression which states that the distance of the two segments are equal, becuase the points divdes them equally. Now, we solve the expression

Now, we have and , we do the same process

Therefore, the circumcenter is at

The centroid of a triangle is defined as

Where

Replacing all values, we have

Therefore, the centroid is at

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