Respuesta :
The coordinates of the circumcenter of this triangle are (3, 2) for the given triangle.
We know that -
The circumcenter is the point of intersection of the perpendicular bisectors of a triangle.
we have the coordinates A(-2, 5) , B(-2, -1), C(8, -1)
Let us find the midpoint AB using the midpoint formula as follows -
M = [tex](\frac{x_1 +x_2}{2}, \frac{y_1 +y_2}{2})[/tex]
substituting the values of A(-2, 5) and B(-2, -1), we get,
M = [tex](\frac{-2-2 }{2}, \frac{5-1}{2})[/tex]
M = (-2, -2)
Hence, the midpoint of segment AB is (-2,-2)
Similarly, we can find the midpoint of segment BC.
The midpoint of segment BC is (3,-1)
Let us now find the equation of the line perpendicular to the segment AB that passes through the point (-2,2).
This line is a horizontal line (parallel to the x-axis) hence, we get the equation y = 2.
Similarly, we can find the equation of the line perpendicular to the segment BC that passes through the point (3,-1).
This line is a vertical line (parallel to the y-axis) hence, we get the equation x = 3.
Finally, we will find the circumcentre of the triangle, which is the intersection of the line perpendicular to segment AB and the line perpendicular to segment BC i.e. (x, y) = (3, 2).
Hence, The coordinates of the circumcenter of this triangle are (3, 2).
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