Question

a line segment with one end at C(6,5) has midpoint m(4,2) determine the coordinates of the other endpoint d

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{6}~,~\stackrel{y_1}{5})\qquad D(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+6}{2}~~,~~\cfrac{y+5}{2} \right)~~=~~\stackrel{\stackrel{Midpoint}{M}}{(4~,~2)}\implies \begin{cases} \cfrac{x+6}{2}=4\\[1em] x+6=8\\ \boxed{x= 2}\\ \cline{1-1} \cfrac{y+5}{2}=2\\[1em] y+5=4\\ \boxed{y=-1} \end{cases}$