Krishna
0

Step 1: Locate the coordinates of the endpoints.

              The given points M (1, 1) and N (2, 3), (4, 5)

              Therefore, (x_1, y_1) = (1, 1), (x_2, y_2) = (2, 3) and (x_3, y_3) = (4, 5).


Step 2: Set up triangle area formula when vertices are given.

              FORMULA: Area of the triangle

               \frac{1}{2} {x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}


Step 3: Plug the corresponding coordinates into the Area of triangle formula.

                               =   \frac{1}{2} {x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}

                               = \frac{1}{2} (1*[3 - 5] + (2)*[5 - 1] + 4*[1 - 3])


Step 4: Simplify further

           NOTE: Apply the BODMAS rules

                            = \frac{1}{2} (1*[-2] + (2)*[4] + 2*[-2])


                             =  \frac{1}{2} (- 2 + 8 - 4)


                             =  \frac{1}{2} (8 - 6])


                             =  \frac{1}{2} (2)


                              = 1


              Hence, area of the triangle = 1 units