we are asked to determine the mid-point of a segment. To do that we will use the following formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ (x_2,y_2)=(2,4) \end{gathered}[/tex]Replacing in the equation:
[tex]M=(\frac{4+2}{2},\frac{2+4}{2})[/tex]Solving the operations:
[tex]\begin{gathered} M=(\frac{6}{2},\frac{6}{2}) \\ M=(3,3) \end{gathered}[/tex]Therefore, the mid-point is (3,3)
