The midpoint of EF is M. The length of EM is 5
Given :
The endpoints of EF are E(2, 3) and F(8, 11).
M is the midpoint of EF
Lets find out the midpoint M using midpoint formula
[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\E (x_1,y_1) is (2,3)\\F(x_2,y_2) is (8,11)[/tex]
Substitute the values inside the formula
[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\(\frac{2+8}{2} ,\frac{3+11}{2} )\\\\(5,7)[/tex]
Midpoint M is (4,7)
Now to find out length of EM, we use distance formula
[tex]Distance = \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\mathrm{The\:distance\:between\:}\left(2,\:3\right)\mathrm{\:and\:}\left(5,\:7\right)\\\sqrt{\left(5-2\right)^2+\left(7-3\right)^2}\\\sqrt{3^2+4^2} \\\sqrt{25}\\5[/tex]
So, length of EM= 5
Learn more : brainly.com/question/18332427
