How do you find the midpoint of (5√2, 2√3), and (√2, 2√3)?

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How do you find the midpoint of (5√2, 2√3), and (√2, 2√3)?

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Answer 1 · 2017-06-14T13:15:26

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

Substituting the values from the points in the problem gives:

$M = (\frac{5 \sqrt{2} + \sqrt{2}}{2}, \frac{2 \sqrt{3} + 2 \sqrt{3}}{2})$ $M = ((color(red)(5sqrt(2)) + color(blue)(sqrt(2)))/2 , (color(red)(2sqrt(3)) + color(blue)(2sqrt(3)))/2)$

$M = (\frac{5 \sqrt{2} + 1 \sqrt{2}}{2}, \frac{2 \sqrt{3} + 2 \sqrt{3}}{2})$ $M = ((color(red)(5sqrt(2)) + color(blue)(1sqrt(2)))/2 , (color(red)(2sqrt(3)) + color(blue)(2sqrt(3)))/2)$

$M = \frac{(5 + 1) \sqrt{2}}{2}, \frac{(2 + 2) \sqrt{3}}{2})$ $M = ((5 + 1)sqrt(2))/2 , ((2 + 2)sqrt(3))/2)$

$M = (\frac{6 \sqrt{2}}{2}, \frac{4 \sqrt{3}}{2})$ $M = ((6sqrt(2))/2 , (4sqrt(3))/2)$

$M = (3 \sqrt{2}, 2 \sqrt{3})$ $M = (3sqrt(2) , 2sqrt(3))$

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How do you find the midpoint of (5√2, 2√3), and (√2, 2√3)?

1 Answer

Explanation:

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