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How do you find the distance between $(-sqrt2,-sqrt2)$ , $(sqrt2, 6sqrt2)$ ?

1 Answer

Jun 13, 2017

$abs((-sqrt2,-sqrt2):(sqrt2,6sqrt2))=color(red)(sqrt(106)$

Explanation:

The easiest way to do this is to observe that the given points are equivalent to $(-1,-1)$ and $(1,6)$ scaled by a factor of $sqrt(2)$

The distance between the given points will be the same as the distance between $(-1,-1)$ and $(1,6)$ multiplied by $sqrt(2)$

The horizontal distance between $(-1,-1)$ and $(1,6)$ is $1-(-1)=2$

The vertical distance between $(-1,-1)$ and $(1,6)$ is $6-(-1)=7$

The diagonal distance between $(-1,-1)$ and $(1,6)$ is given by the Pythagorean Theorem as
$color(white)("XXX")d=sqrt(2^2+7^2)=sqrt(4+49)=sqrt(53)$

and the corresponding diagonal distance between $(-sqrt(2),-sqrt(2))$ and $(sqrt(2),6sqrt(2))$ is
$color(white)("XXX")sqrt(2)d=sqrt(2)*sqrt(53)=sqrt(106)$

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