# What is the distance between (-1,7) and (44,3)?

Mar 29, 2018

See a solution process below:

#### Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{44} - \textcolor{b l u e}{- 1}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{7}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{44} + \textcolor{b l u e}{1}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{7}\right)}^{2}}$

$d = \sqrt{{45}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{2025 + 16}$

$d = \sqrt{2041}$

Or

$d \cong 45.177$

Mar 29, 2018

$\approx 45.18 \text{ to 2 dec. places}$

#### Explanation:

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

•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

$\text{let "(x_1,y_1)=(-1,7)" and } \left({x}_{2} , {y}_{2}\right) = \left(44 , 3\right)$

$\Rightarrow d = \sqrt{{\left(44 + 1\right)}^{2} + {\left(3 - 7\right)}^{2}}$

$\textcolor{w h i t e}{\Rightarrow d} = \sqrt{2041} \approx 45.18$