What are the coordinates of the circumcenter of the triangle ?

The answer to your question is (2, -1)

Step-by-step explanation:

1.- Find half points

AB

Between A and B there are 6 units, then the half point is three units from point A to the right

                                (2, 3)

BC

Between B and C there are 8 units, then the half point is four units below the point B.

                               (5, -1)

AC

Xm = -1 + 5 / 2 = 4 / 2 = 2

Ym = 3 - 5 / 2 = - 2 / 2 = - 1

                               (2, -1)

2.- Find the equations of the mediatrices

AB

          x = 2                     because the line must be perpendicuar to AB

BC

          y = - 1                    because the line must be perpendicular to BC

AC

          slope        m =

                           m =

                           m =

mediatrix AC

                           y + 1 = -4/3 (x -2)

                          3y + 3 = -4x + 8

                           4x + 3y = 8 - 3

                           4x + 3y = 5

3.- Find the circumcenter

When x = 2

                         4(2) + 3y = 5

                           8 + 3y =5

                                 3y = 5 - 8

                                 3y = -3

                                   y = -3/3

                                   y = -1

When y = -1

                        4x + 3(-1) = 5

                        4x - 3 = 5

                        4x = 5 + 3

                        4x = 8

                        x = 8/4

                       x = 2

Circumcenter    (2, -1)

the correct answer is 5

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints