What is the distance between $(5, - 3)$ $(5,-3)$ and $(3, 7)$ $(3,7)$ ?

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What is the distance between $(5, - 3)$ $(5,-3)$ and $(3, 7)$ $(3,7)$ ?

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Answer 1 · 2018-07-25T01:06:42

The distance is $2 \sqrt{26}$ $2sqrt26$ or about $10.198$ $10.198$ (rounded to nearest thousandth's place).

Explanation:

The formula for the distance of 2-dimensional coordinates is: $d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)$

We have the two coordinates, so we can plug in the values for $x$ $x$ and $y$ $y$ :
$d = \sqrt{{(3 - 5)}^{2} + {(7 - (- 3))}^{2}}$ $d = sqrt((3 - 5)^2 + (7 - (-3))^2)$

Now we simplify:
$d = \sqrt{{(- 2)}^{2} + {(10)}^{2}}$ $d = sqrt((-2)^2 + (10)^2)$

$d = \sqrt{4 + 100}$ $d = sqrt(4 + 100)$

$d = \sqrt{104}$ $d = sqrt(104)$

$d = 2 \sqrt{26}$ $d = 2sqrt26$

If you want to leave it in exact form, you can leave the distance as $2 \sqrt{26}$ $2sqrt26$ . However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
$d \approx 10.198$ $d ~~ 10.198$

Hope this helps!

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What is the distance between $(5, - 3)$ $(5,-3)$ and $(3, 7)$ $(3,7)$ ?

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What is the distance between (5,-3)(5,−3)(5,-3) and (3,7) (3,7) (3,7) ?

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What is the distance between $(5, - 3)$ $(5,-3)$ and $(3, 7)$ $(3,7)$ ?