What is the distance of the A(-2,1) and B(5,3)?

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What is the distance of the A(-2,1) and B(5,3)?

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Answer 1 · 2017-03-07T14:59:25

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:

$d = \sqrt{{(5 - - 2)}^{2} + {(3 - 1)}^{2}}$ $d = sqrt((color(red)(5) - color(blue)(-2))^2 + (color(red)(3) - color(blue)(1))^2)$

$d = \sqrt{{(5 + 2)}^{2} + {(3 - 1)}^{2}}$ $d = sqrt((color(red)(5) + color(blue)(2))^2 + (color(red)(3) - color(blue)(1))^2)$

$d = \sqrt{7^{2} + 2^{2}}$ $d = sqrt(7^2 + 2^2)$

$d = \sqrt{49 + 4}$ $d = sqrt(49 + 4)$

$d = \sqrt{53} = 7.280$ $d = sqrt(53) = 7.280$

The distance is $\sqrt{53}$ $sqrt(53)$ or $7.280$ $7.280$ rounded to the nearest thousandth

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What is the distance of the A(-2,1) and B(5,3)?

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