Question

The line AB has midpoint (4,2). A has coordinates (7,3). Find the coordinates of B

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{3})\qquad B(\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 +7}{2}~~~ ,~~~ \cfrac{ y +3}{2} \right) ~~ = ~~\stackrel{\textit{\large Midpoint} }{(4~~,~~2)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +7 }{2}=4\implies x+7=8\implies \boxed{x=1} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +3 }{2}=2\implies y+3=4\implies \boxed{y=1}`