How do you find the midpoint of the line segment joining (2,-4) and (5,-2)?

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Answer 1 · 2018-01-04T12:48:51

See a solution process below:

The formula 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:

$(x_{1}, y_{1})$ $(color(red)(x_1), color(red)(y_1))$ and $(x_{2}, y_{2})$ $(color(blue)(x_2), color(blue)(y_2))$

Substituting the values from the points in the problem gives:

$M = (\frac{2 + 5}{2}, \frac{- 4 + - 2}{2})$ $M = ((color(red)(2) + color(blue)(5))/2 , (color(red)(-4) + color(blue)(-2))/2)$

$M = (\frac{7}{2}, - \frac{6}{2})$ $M = (7/2 , -6/2)$

$M = (\frac{7}{2}, - 3)$ $M = (7/2 , -3)$