Question

Find the midpoint of the segment with endpoints of −11 + i and −4 + 4i.

Answer 1

`\bf \begin{cases} -11+i\implies -11+1i\\ \qquad (-11,1)\\ -4+4i\\ \qquad (-4,4) \end{cases} \\\\\\ ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-11}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)`

`\bf \left( \cfrac{-4-11}{2}~~,~~ \cfrac{4+1}{2}\right)\implies \left(-(15)/(2)~,~(5)/(2) \right)\implies \left(-7(1)/(2)~,~2(1)/(2) \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -7(1)/(2)+2(1)/(2)i~\hfill`

Answer 2

(-11 +-4)/2 = -15/2

(i+4i)/2= 5/2 i

the midpoint is (-15/2, 5/2 i)

or (-7.5 ,2.5i)