# What is the distance between (-7,6,10) and (7,-4,9)?

Mar 29, 2018

#### Answer:

distance $= 3 \sqrt{33} \approx 17.2$ square units

#### Explanation:

We seek the distance $d$, say, between the coordinates $\left(- 7 , 6 , 10\right)$ and $\left(7 , - 4 , 9\right)$? in euclidean space.

Applying Pythagoras theorem in $3$-Dimensions we have:

${d}^{2} = {\left(- 7 - 7\right)}^{2} + {\left(6 - \left(- 4\right)\right)}^{2} + {\left(10 - 9\right)}^{2}$
$\setminus \setminus \setminus \setminus = {\left(- 14\right)}^{2} + {\left(10\right)}^{2} + {\left(1\right)}^{2}$
$\setminus \setminus \setminus \setminus = 196 + 100 + 1$
$\setminus \setminus \setminus \setminus = 297$

Thus:

$d = \sqrt{297} \setminus \setminus \setminus$ (NB - we seek the positive solution)
$\setminus \setminus = \sqrt{9 \cdot 33}$
$\setminus \setminus = 3 \sqrt{33}$
$\setminus \setminus \approx 17.2$