# How do you find the distance between O(-2, 10) and P(-8,3)?

##### 3 Answers
Jan 6, 2018

$\sqrt{85} \approx 9.22 \text{ to 2 dec. places}$

#### Explanation:

$\text{ find the distance (d) using the "color(blue)"distance formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let "(x_1,y_1)=(-2,10)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 8 , 3\right)$

$d = \sqrt{{\left(- 8 - \left(- 2\right)\right)}^{2} + {\left(3 - 10\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{36 + 49} = \sqrt{85} \approx 9.22$

Jan 6, 2018

distance$= \sqrt{85}$ units ~9.22 units

#### Explanation:

distance$= \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
distance$= \sqrt{{\left(- 8 - \left(- 2\right)\right)}^{2} + {\left(3 - 10\right)}^{2}}$
distance$= \sqrt{{\left(- 6\right)}^{2} + {\left(- 7\right)}^{2}}$
distance$= \sqrt{85}$ units

I hope that helps :)

Jan 6, 2018

Giving an understanding to the distance formula...

#### Explanation:

Explanation to prior answer.

The 'color(red)("distance"' formula as stated is just an adaptation of pythagerous' theorem

Let there be two different points $\left({x}_{1} , {y}_{1}\right) \text{ and } \left({x}_{2} , {y}_{2}\right)$:

Now drawring dotted lines... We see this is a right angled trianlge, were we can use pythagerouses theorem...