# What is the distance between (-7, 7)  and (5, 6) ?

Feb 10, 2017

The distance between the two points is:

$\sqrt{145} \approx 12.04$ to 2 decimal places.

#### Explanation:

When you are not sure of something make a quick sketch so you can see more clearly what the situation is.

Let point 1 be ${P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(- 7 , 7\right)$
Let point 2 be ${P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(5 , 6\right)$
Let the direct distance between the two points be $d$

The change in down is: $\text{y_2-y_1" "=" "7-6" "=" } 1$
The change in along is: $\text{x_2-x_1" "=" "5-(-7)" "=" } 12$

Using Pythagoras ${d}^{2} = {12}^{2} + {1}^{2}$

$d = \sqrt{145}$

The only factors of 145 are 1, 5, 9, 145,

So we can not break this down into simplified surds (roots)

So we represent the solution as $\sqrt{145}$ which is an exact value or as a rounded decimal which is not exact.

$\implies d = \sqrt{145} \approx 12.04$ to 2 decimal places.

The sign of $\approx$ means approximately