Question

Find the coordinates of the midpoint of each segment. The coordinates of the endpoints are given

J(2 1/2, -1/4), K(3 1/4, -1)

Answer 1

let's first off, convert the mixed fractions to improper, and then get the midpoint.

`\bf \stackrel{mixed}{2(1)/(2)}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}}~\hfill \stackrel{mixed}{3(1)/(4)}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ J(\stackrel{x_1}{(5)/(2)}~,~\stackrel{y_1}{-(1)/(4)})\qquad K(\stackrel{x_2}{(13)/(4)}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)`

`\bf \left( \cfrac{~~(13)/(4)+(5)/(2)~~}{2}~~,~~\cfrac{~~-1-(1)/(4)~~}{2} \right)\implies \left( \cfrac{~~(13+10)/(4)~~}{2}~~,~~\cfrac{~~(-4-1)/(4)~~}{2} \right) \\\\\\ \left( \cfrac{~~(23)/(4)~~}{(2)/(1)}~~,~~\cfrac{~~(-5)/(4)~~}{(2)/(1)} \right)\implies \left( \cfrac{23}{8}~~,~-\cfrac{5}{8} \right)`