How do you find the midpoint of the line segment with endpoints (5, 12 and (7, -5)?

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Answer 1 · 2016-12-26T03:58:40

The midpoint of this line segment is $(6, \frac{7}{2})$ $(6, 7/2)$

The equation to find the mid-point of a line segment give the two end points is:

$M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)$

Where $M$ $M$ is the midpoint and the given points are:

$color(red)((x_1, y_1))$ and $color(blue)((x_2, y_2))$

Substituting the points from the problems allows us to solve for $M$ :

$M = ((color(red)(5) + color(blue)(7))/2 , (color(red)(12) + color(blue)(-5))/2)$

$M = (12/2 , 7/2)$

$M = (6, 7/2)$