Answer:
<h2>1.</h2>
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
<h2>2.</h2>
The centroid of a triangle is defined as
Where
Replacing all values, we have
Therefore, the centroid is at