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How do you find the distance between (-2,4), (5,8)?

1 Answer

Dec 26, 2016

$| (- 2, 4) : (5, 8) | = \sqrt{65}$ $abs((-2,4):(5,8))=color(green)(sqrt(65))$

Explanation:

The horizontal distance ( $Deltax$ )between $(-2,4)$ and $(5,8)$ is the absolute value of the difference between the $x$ components of the coordinates:
$color(white)("XXX")Deltax = abs(5-(-2))=7$

Similarly, the vertical distance ( $Deltay$ )between $(-2,4)$ and $(5,8)$ is the absolute value of the difference between the $y$ components of the coordinates:
$color(white)("XXX")Deltax = abs(8-4)=4$

Using the Pythagorean Theorem the distance between $(-2,4)$ and $(5,8)$ is
$color(white)("XXX")d=sqrt(7^2+4^2)=sqrt(65)$

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