Question

The endpoints of EF are E(2, 3) and F(8, 11). The midpoint of EF is M. Find the length of EM.

Answer 1

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

$(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\E (x_1,y_1) is (2,3)\\F(x_2,y_2) is (8,11)$

Substitute the values inside the formula

$(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\(\frac{2+8}{2} ,\frac{3+11}{2} )\\\\(5,7)$

Midpoint M is (4,7)

Now to find out length of EM, we use distance formula

$Distance = \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\\mathrm{The\:distance\:between\:}\left(2,\:3\right)\mathrm{\:and\:}\left(5,\:7\right)\\\sqrt{\left(5-2\right)^2+\left(7-3\right)^2}\\\sqrt{3^2+4^2} \\\sqrt{25}\\5$

So, length of EM= 5

Learn more :  brainly.com/question/18332427