# What is the distance between (1,-3,-5) and (-2,3-,4)?

Jul 17, 2018

The distance is $3 \sqrt{10}$ or about $9.49$ (rounded to nearest hundredth's place).

#### Explanation:

The formula for the distance for 3-dimensional coordinates is similar or 2-dimensional; it is: $d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

We have the two coordinates, so we can plug in the values for $x$, $y$, and $z$:
$d = \sqrt{{\left(- 2 - 1\right)}^{2} + {\left(- 3 - \left(- 3\right)\right)}^{2} + {\left(4 - \left(- 5\right)\right)}^{2}}$

(I wasn't sure if the $3 -$ meant $3$ or $- 3$, so I assumed it was $- 3$)

Now we simplify:
$d = \sqrt{{\left(- 3\right)}^{2} + {\left(0\right)}^{2} + {\left(9\right)}^{2}}$

$d = \sqrt{9 + 0 + 81}$

$d = \sqrt{90}$

$d = 3 \sqrt{10}$

If you want to leave it in exact form, you can leave the distance as $3 \sqrt{10}$. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
$d \approx 9.49$

Hope this helps!