How do you find the midpoint of A(-4,-2) and B(4,3)?

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Answer 1 · 2018-06-12T18:35:01

$(0, \frac{1}{2})$ $(0,\frac{1}{2})$

Work out the centers of the x and the y coordinates individually such that the center is:

$(\frac{- 4 + 4}{2}, \frac{- 2 + 3}{2})$ $(\frac{-4+4}{2},\frac{-2+3}{2})$

Simplify it to:
$(0, \frac{1}{2})$ $(0,\frac{1}{2})$

Answer 2 · 2018-06-12T18:35:10

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:

$M = (\frac{- 4 + 4}{2}, \frac{- 2 + 3}{2})$ $M = ((color(red)(-4) + color(blue)(4))/2 , (color(red)(-2) + color(blue)(3))/2)$

$M = (\frac{0}{2}, \frac{1}{2})$ $M = (0/2 , 1/2)$

$M = (0, \frac{1}{2})$ $M = (0, 1/2)$