Midpoint of a Line Segment
Midpoint of a Line Segment
\(M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)
Average each pair of coordinates separately.
For endpoints \(A(x_1,y_1)\) and \(B(x_2,y_2)\):
Average each pair of coordinates separately.
Example
The midpoint of \(A(-3,5)\) and \(B(7,-1)\) is \(M\left(\dfrac{-3+7}{2},\dfrac{5+(-1)}{2}\right)=(2,2)\).
Reverse: given \(A(-3,5)\) and midpoint \(M(2,2)\), \(B=(2(2)-(-3),\,2(2)-5)=(7,-1)\).
Exam check: add the coordinates and halve; do not subtract. To find an endpoint, use \(x_B=2x_M-x_A\) and \(y_B=2y_M-y_A\).
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