Question

Find the distance between the points $(2,3)$and $(4,1)$

Answer 1

Solve for the distance between two points

Let $\left(x_1,y_1\right)=(2,3)$and $\left(x_2,y_2\right)=(4,1)$

Let $d$ be the distance between two points and distance formula to find the distance between two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

$\mathbf{d}\mathbf{=}\sqrt{\mathbf{(}{\mathbf{x}}_{\mathbf{2}}\mathbf{-}{\mathbf{x}}_{\mathbf{1}}{\mathbf{)}}^{\mathbf{2}}\mathbf{+}\mathbf{(}{\mathbf{y}}_{\mathbf{2}}\mathbf{-}{\mathbf{y}}_{\mathbf{1}}{\mathbf{)}}^{\mathbf{2}}}$

Substitute the values in formula

$\Rightarrow$$d=\sqrt{{(4-2)}^2+(1-3{)}^2}$

$\Rightarrow$ $=\sqrt{{\left(2\right)}^2+(-2{)}^2}$

$\Rightarrow$ $=\sqrt{8}$

$\Rightarrow$$d=2\sqrt{2}$

Hence the distance between the points $(2,3)$ and $(4,1)$ is $2\sqrt{2}$.