Question

(-2,1) is the midpoint between (-4,4) and (x2, y2). Find (x2, y2).

Answer 1

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{x_2}~,~\stackrel{y_2}{y_2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x_2-4}{2}~~,~~\cfrac{y_2+4}{2} \right)~~=~~\stackrel{midpoint}{(-2~,~1)}\implies \begin{cases} \cfrac{x_2-4}{2}=-2\\[1em] x_2-4=-4\\ \boxed{x_2=0}\\ \cline{1-1} \cfrac{y_2+4}{2}=1\\[1em] y_2+4=2\\ \boxed{y_2=-2} \end{cases}`