What is the distance between $(–6, 3, 4)$ and $(–5, –1, 1)$ ?

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Answer 1 · 2017-12-19T23:56:45

$sqrt(26)$

You may be familiar with the two-dimensional distance formula, which tells us that the distance between $(x_1, y_1)$ and $(x_2, y_2)$ is:

$sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

There is a similar formula for three dimensions for the distance between $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ , namely:

$sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$

So in our example, the distance between $(x_1, y_1, z_1) = (-6, 3, 4)$ and $(x_2, y_2, z_2) = (-5, -1, 1)$ is:

$sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$

$= sqrt(((-5)-(-6))^2+((-1)-3)^2+(1-4)^2)$

$= sqrt(1^2+(-4)^2+(-3)^2)$

$= sqrt(1+16+9)$

$= sqrt(26)$

What is the distance between (–6, 3, 4) (–6, 3, 4) and (–5, –1, 1) (–5, –1, 1) ?