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  • 14-09-2022
  • Mathematics
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B is the midpoint of AB. If the coordinates of B are (11,20) and A are (3,8) what are the coordinates of C?

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jdoe0001 jdoe0001
  • 14-09-2022

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad C(\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 +3}{2}~~~ ,~~~ \cfrac{ y +8}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE B}}{(11~~,~~20)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +3}{2}=11\implies x+3=22\implies \boxed{x=19} \\\\\\ \cfrac{ y +8}{2}=20\implies y+8=40\implies \boxed{y=32}[/tex]

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