Question

The midpoint of GH is M(3, 0). One endpoint is G(1, 0). Find the coordinates of the other endpoint H.

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ G(\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad H(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+1}{2}~~,~~\cfrac{y+0}{2} \right)~~=~~\stackrel{\stackrel{Midpoint}{M}}{(3~,~0)}\implies \begin{cases} \cfrac{x+1}{2}=3\\[1em] x+1=6\\ \boxed{x=5}\\ \cline{1-1} \cfrac{y+0}{2}=0\\[1em] \boxed{y=0} \end{cases}$