The distance between -5 and 8 is 13.
The distance between -2 and 4 is 6.
These two distances, including the hypotenuse which is the distance you want to discover - form a right angled triangle. The adjacent side of this right angled triangle has a length of 13, whilst its opposite side has a length of 6.
If you want to find the distance between (-5, 4) and (8, -2), you simply measure the hypotenuse of this invisible right angled triangle which has been formed. Let's call the length of this hypotenuse "d".
We shall use Pythagoras's theorem to produce our result:
[tex]{ d }^{ 2 }={ 13 }^{ 2 }+{ 6 }^{ 2 }\\ \\ d=\sqrt { { 13 }^{ 2 }+{ 6 }^{ 2 } } \\ \\ \therefore \quad d=\sqrt { 205 } [/tex]
[*Complete answer derived on a calculator]
This means that the distance between (-5, 4) and (8, -2) is [tex] \sqrt{205} [/tex]. [tex] \sqrt{205} [/tex] is approximately equal to 14.3.
