The midpoint of overline AB is M(3, 0) If the coordinates of A are (2, 4) what are the coordinates of B?

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Jingwen asked Jul 23, 2023

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36 votes

The midpoint of overline AB is M(3, 0) If the coordinates of A are (2, 4) what are the coordinates of B?

The midpoint of overline AB is M(3, 0) If the coordinates of A are (2, 4) what are-example-1

Mathematics
high-school

Jingwen asked Jul 23, 2023

by Jingwen

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1 Answer

13 votes

Answer: B(4,-4)

Explanation:

M(3,0) A(2,4) B(x,y)=?

$\displaystyle\\x_M=(x_A+x_B)/(2) \\\\Multiply\ both\ parts\ of\ the\ equation\ by \ 2:\\2x_M=x_A+x_B\\2x_M-x_A=x_A+x_B-x_A\\2x_M-x_A=x_B\\x_M=3\ \ \ \ \ x_A=2\\Hence,\\2*3-2=x_B\\6-2=x_B\\4=x_B\\Similarly:\\2y_M-y_A=y_B\\y_m=0\ \ \ \ \ y_A=4\\Hence,\\2*0-4=y_B\\0-4=y_B\\-4=y_B\\Thus,\ B(4,-4)$