# What is the distance between (-5,2 )  and  (4, 7) ?

Jan 5, 2016

$\sqrt{106}$ ≈ 10.3 (1 decimal place )

#### Explanation:

To find the distance (d ) between 2 coordinate points $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$

Use the distance formula which is given as

 color(red)( d = sqrt ((x_2 - x_1 )^2 + ( y_2 - y_1 )^2

For the coordinate pairs given let $\left(- 5 , 2\right) = \left({x}_{1} , {y}_{1}\right) , \left(4 , 7\right) = \left({x}_{2} , {y}_{2}\right)$

substituting into the formula

 d = sqrt (4 - (-5)^2 + (7 - 2 )^2

 = sqrt( 9^2 + 5^2

=$\sqrt{81 + 25} = \sqrt{106}$ ≈ 10.3 (1 decimal place )