How do you use the distance formula to find the distance between (-10, 2) and (-4,-6)?

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How do you use the distance formula to find the distance between (-10, 2) and (-4,-6)?

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Answer 1 · 2017-02-26T14:09:40

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:

$d = \sqrt{{(- 4 - - 10)}^{2} + {(- 6 - 2)}^{2}}$ $d = sqrt((color(red)(-4) - color(blue)(-10))^2 + (color(red)(-6) - color(blue)(2))^2)$

$d = \sqrt{{(- 4 + 10)}^{2} + {(- 6 - 2)}^{2}}$ $d = sqrt((color(red)(-4) + color(blue)(10))^2 + (color(red)(-6) - color(blue)(2))^2)$

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

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

$d = \sqrt{100} = 10$ $d = sqrt(100) = 10$

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How do you use the distance formula to find the distance between (-10, 2) and (-4,-6)?

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