How do you find the distance between (4,2), (6,-2/3)?

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How do you find the distance between (4,2), (6,-2/3)?

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Answer 1 · 2017-05-30T16:14:28

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:

$d = \sqrt{{(6 - 4)}^{2} + {(- \frac{2}{3} - 2)}^{2}}$ $d = sqrt((color(red)(6) - color(blue)(4))^2 + (color(red)(-2/3) - color(blue)(2))^2)$

$d = \sqrt{{(6 - 4)}^{2} + {(- \frac{2}{3} - (\frac{3}{3} \times 2))}^{2}}$ $d = sqrt((color(red)(6) - color(blue)(4))^2 + (color(red)(-2/3) - (3/3 xx color(blue)(2)))^2)$

$d = \sqrt{{(6 - 4)}^{2} + {(- \frac{2}{3} - \frac{6}{3})}^{2}}$ $d = sqrt((color(red)(6) - color(blue)(4))^2 + (color(red)(-2/3) - 6/3)^2)$

$d = \sqrt{2^{2} + {(- \frac{8}{3})}^{2}}$ $d = sqrt(2^2 + (-8/3)^2)$

$d = \sqrt{4 + \frac{64}{9}}$ $d = sqrt(4 + 64/9)$

$d = \sqrt{(\frac{9}{9} \times 4) + \frac{64}{9}}$ $d = sqrt((9/9 xx 4) + 64/9)$

$d = \sqrt{\frac{36}{9} + \frac{64}{9}}$ $d = sqrt(36/9 + 64/9)$

$d = \sqrt{\frac{100}{9}}$ $d = sqrt(100/9)$

$d = \frac{\sqrt{100}}{\sqrt{9}}$ $d = sqrt(100)/sqrt(9)$

$d = \frac{10}{3}$ $d = 10/3$

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How do you find the distance between (4,2), (6,-2/3)?

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