Question

How do you find the distance between the pair of points $\left(6,2\right)$ and $\left(18,11\right)$?

Answer 1

Finding the distance between two given points:

It's known that from the distance formula, the distance between two-point $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$.

So in the given question

$\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\Rightarrow \left(6,2\right)$

$\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)\Rightarrow \left(18,11\right)$

Distance $\left(\mathrm{d}\right)$is can be calculated as:

$\begin{array}{rcl}d& =& \sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ & =& \sqrt{{\left(18-6\right)}^2+{\left(11-2\right)}^2}\\ & =& \sqrt{{\left(12\right)}^2+{\left(9\right)}^2}\\ & =& \sqrt{144+81}\\ & =& \sqrt{225}\\ & =& 15\end{array}$

Hence, the distance between two given points is $15$.