How do you find the distance between the points (5,-1), (11,7)?

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How do you find the distance between the points (5,-1), (11,7)?

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Answer 1 · 2017-07-17T21:18:11

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:

$d = \sqrt{{(11 - 5)}^{2} + {(7 - - 1)}^{2}}$ $d = sqrt((color(red)(11) - color(blue)(5))^2 + (color(red)(7) - color(blue)(-1))^2)$

$d = \sqrt{{(11 - 5)}^{2} + {(7 + 1)}^{2}}$ $d = sqrt((color(red)(11) - color(blue)(5))^2 + (color(red)(7) + color(blue)(1))^2)$

$d = \sqrt{6^{2} + 8^{2}}$ $d = sqrt(6^2 + 8^2)$

$d = \sqrt{36 + 64}$ $d = sqrt(36 + 64)$

$d = \sqrt{100}$ $d = sqrt(100)$

$d = 10$ $d = 10$

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How do you find the distance between the points (5,-1), (11,7)?

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