How do you find the distance between the points (-12,-8), (3,11)?

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How do you find the distance between the points (-12,-8), (3,11)?

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Answer 1 · 2017-02-27T23:27:00

See the entire solution process below:

Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ $d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)$

Substituting the values from the points in the problem gives:

$d = \sqrt{{(3 - - 12)}^{2} + {(11 - - 8)}^{2}}$ $d = sqrt((color(red)(3) - color(blue)(-12))^2 + (color(red)(11) - color(blue)(-8))^2)$

$d = \sqrt{{(3 + 12)}^{2} + {(11 + 8)}^{2}}$ $d = sqrt((color(red)(3) + color(blue)(12))^2 + (color(red)(11) + color(blue)(8))^2)$

$d = \sqrt{15^{2} + 19^{2}}$ $d = sqrt(15^2 + 19^2)$

$d = \sqrt{225 + 361}$ $d = sqrt(225 + 361)$

$d = \sqrt{586} = 24.207$ $d = sqrt(586) = 24.207$ rounded to the nearest thousandth.

The distance between the two points is $\sqrt{586}$ $sqrt(586)$ or $24.207$ $24.207$ rounded to the nearest thousandth.

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How do you find the distance between the points (-12,-8), (3,11)?

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