Question

The distance between the points (0, 5) and (5, 0) is __________.

Answer 1

The distance between $\left(x_1,y_1\right)\mathrm{and}\left(x_2,y_2\right)\mathrm{is}\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$.

Therefore, the distance between the points (0, 5) and (5, 0)$=\sqrt{{\left(5-0\right)}^2+{\left(0-5\right)}^2}$
$$\begin{gathered} =\sqrt{{\left(5\right)}^2+{\left(-5\right)}^2} \\ =\sqrt{25+25} \\ =\sqrt{50} \\ =5\sqrt{2} \end{gathered}$$

Hence, the distance between the points (0, 5) and (5, 0) is $\underline{5\sqrt{2}\mathrm{units}}.$