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Midpoint of an interval

The midpoint of an interval with endpoints \(P(x_1, y_1)\) and \(Q(x_2, y_2)\) has coordinates

\((\dfrac{x_1 + x_2}{2},\ \dfrac{y_1 + y_2}{2})\).

The coordinates are found by calculating the average of the x-coordinates and the average of the y-coordinates.

Example 3

Find the coordinates of the midpoint of the line interval joining the points (6, 8) and (−3, 2).


The midpoint M has coordinates

\((\dfrac{6 + (-3)}{2},\ \dfrac{8 + 2}{2}) = (\dfrac{3}{2},\ 5)\).

Cartesian plane. Points (–3, 2), M(1.5, 5), (6, 8) shown.
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