Krishna
0

Step 1: Name those given vertices and recall "what is a circumcenter"  

            NOTE: The circumcenter is the point of intersection of the axes that passes

            perprendicularly trough the midpoint of a side of that traingle.

                  A=(−3,−3), B=(5,1), C=(11,−1).


Step 2: Calculate the midpoints of the sides

            NOTE: Note down the endpoints (x_1, y_1) and (x_2, y_2) from the given

            points. And substitute the values into the midpoint formula.


            [FORMULA: The midpoint formula is

            M = \left(\frac{\left(x_1+x_2\right)}{2},\frac{\left(y_1+y_2\right)}{2}\right)

              where M is the midpoint of a line segment with endpoints at  

                  (x_1, y_1) and (x_2, y_2).


Step 3: Find the line perpendicular to side (AB) that passes through mid-point

            FORMULA: Equation of the line

                                     (y - y_1) = m (x - x_1)

                                    Slope m = \frac{y_2 - y_1}{x_2 - x_1}

          NOTE: Two lines with slopes m_1and m_2 are perpendicular if

                     m_1* m_2 = -1

                      

Step 4: In the same way calculate the line perpendicular to another side (BC) that    passes through mid-point.


Step 5: Solve the two equations to find the intersection point of the two perpendicular lines of the triangle sides.

              EXAMPLE:  y = −2x + 1

                                    y = 3x − 24

                              Solve the equations for x.  L.H.S are equal so equate the R.H.S

                                  −2x + 1 = 3x − 24

                                      x = 5

                      x=5, plugging it in y= −2x + 1

                            y = -2 (5) + 1

                            y = -9

  So, Circumcenter  = (x, y) = (5, -9)