Krishna
0

Step 1: Determine the mid points on the required line.

            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 = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) = (\frac{1 + 4}{2}, \frac{2 + 11}{2})

                          M = (\frac{5}{2}, \frac{13}{2})

            where M is the midpoint of a line segment with endpoints  

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


Step 2: Calculate the slope of the line perpendicular to the perpendicular bisector

             NOTE: m = \frac{y_2 - y_1}{x_2 - x_1}

            EXAMPLE: Line AC is perpendicular to the altitude

                              A(1, 2), C(4, 11)

                              m = \frac{11 - 2}{4 - 1} = 3

  

Step 2: Find the slope of the perpendicular bisector

          NOTE: Perpendicular gradients are connected by m_1 m_2 = - 1

          EXAMPLE: Perpendicular bisector slop m(3) = -1

                                                   m = \frac{-1}{3}


Step 3: Calculate the equation of the line containing the perpendicular bisector from the midpoint and the slope.

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

              EXAMPLE: midpoint   (\frac{5}{2}, \frac{13}{2}) and slope   m = \frac{-1}{3}

                                y-\frac{13}{2}=\frac{-1}{3}(x-\frac{5}{2})

                                              

Step 4:Substitute the known values in the line equation and simplify

                    EXAMPLE: 3(y - \frac{13}{2}) = -1(x - \frac{5}{2})

                                          3y - 3 * \frac{13}{2} = -x + \frac{5}{2}

                                          6y - 39=  -2x + 5

                                          6y + 2x = 44

                                            3y + x = 22


Step 5: Do this for the other two medians as well.