What is the distance between $(23, 43)$ $(23,43)$ and $(34, 38)$ $(34,38)$ ?

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What is the distance between $(23, 43)$ $(23,43)$ and $(34, 38)$ $(34,38)$ ?

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Answer 1 · 2018-07-10T14:00:54

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:

$d = \sqrt{{(34 - 23)}^{2} + {(38 - 43)}^{2}}$ $d = sqrt((color(red)(34) - color(blue)(23))^2 + (color(red)(38) - color(blue)(43))^2)$

$d = \sqrt{11^{2} + {(- 5)}^{2}}$ $d = sqrt(11^2 + (-5)^2)$

$d = \sqrt{121 + 25}$ $d = sqrt(121 + 25)$

$d = \sqrt{146}$ $d = sqrt(146)$

Or, approximately:

$d ≅ 12.083$ $d ~= 12.083$

Answer 2 · 2018-07-11T00:05:07

$\approx 12.08$ $~~12.08$

Explanation:

The key realization is that we can use the distance formula

$sqrt((Deltax)^2+(Deltay)^2)$

Where the Greek letter Delta means "change in". We just need to figure out how much our $x$ and $y$ change by, respectively.

We go from $x=23$ to $x=34$ , so we can say $Deltax=11$ .

We go from $y=43$ to $y=38$ , so we can say $Deltax=-5$ .

Plugging these into our formula, we get

$sqrt((11)^2+(-5)^2)$

$=>sqrt(121+25)=sqrt(146)~~12.08$

Hope this helps!

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What is the distance between $(23, 43)$ $(23,43)$ and $(34, 38)$ $(34,38)$ ?

2 Answers

Explanation:

Explanation:

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