03Dmidpoint

= The Midpoint of a Line Segment =

The ** midpoint ** of a line segment is exactly half-way between each endpoint.

Consider two points A and B on a straight line (shown right)
 * A(x 1, y 1 )
 * B(x 2, y 2 )

The midpoint (M) will be exactly half-way between A and B.

The ** x-coordinate of M ** will be half-way between x 1 and x 2.
 * This is the __average__ (mean) of x 1 and x 2

math . \qquad \qquad x_m = \dfrac{x_1+x_2}{2} math

The ** y-coordinate of M ** will be half-way between y 1 and y 2.
 * This is the __average__ (mean) of y 1 and y 2

math . \qquad \qquad y_m = \dfrac{y_1+y_2}{2} math

Hence the ** coordinates of M ** are given by

math . \qquad \qquad \left( \dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2} \right) math

** Example 1 **
Find the coordinates of the midpoint of the line segment joining (–1, 6) and (5, 8)


 * Solution: **


 * (–1, 6) = (x 1, y 1 )
 * (5, 8) = (x 2, y 2 )

Coordinates of the midpoint are: math \\ . \qquad \;\; \left( \dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2} \right) \\. \\ . \qquad =\left( \dfrac{(-1) + 5}{2}, \; \dfrac{6 + 8}{2} \right) \\. \\ . \qquad = \left( \dfrac{4}{2}, \; \dfrac{14}{2} \right) \\. \\ . \qquad = \big( 2, \; 7\big) math

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