Answer:
[tex]\boxed {\boxed {\sf (4,6) }}[/tex]
Step-by-step explanation:
The midpoint formula is:
[tex](\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2} )[/tex]
where (x₁, y₁) and (x₂, y₂) are the points are the endpoints.
We are given the points: (2,4) and (6,8). Therefore,
[tex]x_1=2\\y_1=4 \\x_2=6 \\y_2=8[/tex]
Substitute the values into the formula.
[tex](\frac{2+6}{2},\frac{4+8}{2})[/tex]
Find the x coordinate first.
[tex](4, \frac{4+8}{2})[/tex]
Find the y-coordinate next.
[tex](4,6)[/tex]
The midpoint of EF is (4,6)
[tex] \large\bf \underline{Given:-}[/tex]
[tex] \large\bf \underline{To \: Find:-}[/tex]
[tex]\large\bf \underline{ Solution:-}[/tex]
[tex] \sf \: Here, \\ \sf (2,4) = ( x_{1}, y_{1}) \\ \sf (6,8) = ( x_{ 2}, y_{2})[/tex]
We know that,
[tex] \sf \bigstar \: Formula \: to \: find \: the \: midpoint = ( \frac{ x_{1} + x_{2} }{2}, \: \frac{ y_{1} + y_{2} }{2} )[/tex]
[tex] \sf \: Hence, \: The \: midpoint \: of \: EF \: is = ( \frac{2 + 6}{2} , \frac{4 + 8}{2} )[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = ( \frac{8}{2} , \frac{12}{2} )[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf =( 4,6)[/tex]
[tex] \bf \: Therefore, the \: midpoint \: of \: EF \: is \: (4,6).[/tex]
