How do you find the distance between (-4,5) and (8,-4)?

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How do you find the distance between (-4,5) and (8,-4)?

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Answer 1 · 2017-05-27T20:18:31

See a 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:

$d = \sqrt{{(8 - - 4)}^{2} + {(- 4 - 5)}^{2}}$ $d = sqrt((color(red)(8) - color(blue)(-4))^2 + (color(red)(-4) - color(blue)(5))^2)$

$d = \sqrt{{(8 + 4)}^{2} + {(- 4 - 5)}^{2}}$ $d = sqrt((color(red)(8) + color(blue)(4))^2 + (color(red)(-4) - color(blue)(5))^2)$

$d = \sqrt{12^{2} + {(- 9)}^{2}}$ $d = sqrt(12^2 + (-9)^2)$

$d = \sqrt{144 + 81}$ $d = sqrt(144 + 81)$

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

$d = 15$ $d = 15$

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How do you find the distance between (-4,5) and (8,-4)?

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