# What is the distance between (7,9,4) and (3,-5,1)?

Jan 20, 2016

$L = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

I will let you finish this.

#### Explanation:

$\textcolor{b l u e}{\text{Step 1}}$

$\textcolor{b r o w n}{\text{First consider the horizontal plane of x,y}}$

The image of strait line between these point can be projected onto the x,y plane. This, when considered in relation to the axis forms a triangle.

So you can determine the length of the projection on that plane by using Pythagoras.

$\textcolor{b l u e}{\text{Step 2}}$

$\textcolor{b r o w n}{\text{You now consider the z-axis.}}$

The image on the xy plane is considered as the adjacent of a triangle and the z-axis as the opposite. Again you can use Pythagoras. This time the result is the actual magnitude of the distance between the points.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let L be the length of the strait line between the points.

Then $L = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

I will let you work that out!