How do you find the midpoint of the segment with the endpoints (2/3,9/2) and (1/3,11/2)?

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How do you find the midpoint of the segment with the endpoints (2/3,9/2) and (1/3,11/2)?

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Answer 1 · 2017-06-06T20:10:06

See a solution process below:

Explanation:

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 $(x_{2}, y_{2})$ $(color(blue)(x_2, y_2))$

Substituting the values from the points in the problem gives:

$M = (\frac{\frac{2}{3} + \frac{1}{3}}{2}, \frac{\frac{9}{2} + \frac{11}{2}}{2})$ $M = ((color(red)(2/3) + color(blue)(1/3))/2 , (color(red)(9/2) + color(blue)(11/2))/2)$

$M = ⎛ ⎜ ⎝ \frac{(\frac{2 + 1}{3})}{2}, \frac{\frac{9 + 11}{2}}{2} ⎞ ⎟ ⎠$ $M = ((((color(red)(2) + color(blue)(1))/3))/2 , ((color(red)(9) + color(blue)(11))/2)/2)$

$M = (\frac{\frac{3}{3}}{2}, \frac{\frac{20}{2}}{2})$ $M = ((3/3)/2 , ((20)/2)/2)$

$M = (\frac{1}{2}, \frac{10}{2})$ $M = (1/2 , 10/2)$

$M = (\frac{1}{2}, 5)$ $M = (1/2 , 5)$

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How do you find the midpoint of the segment with the endpoints (2/3,9/2) and (1/3,11/2)?

1 Answer

Explanation:

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