Question

what is the distance between the point A(c,0) and B(0, -c)?/

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{points}\mathrm{are}\mathrm{A}\left(\mathrm{c},0\right)\mathrm{and}\mathrm{B}\left(0,-\mathrm{c}\right). \\ \mathrm{Now},\mathrm{we}\mathrm{know}\mathrm{that}\mathrm{distance}\mathrm{between}\mathrm{points}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\mathrm{and}\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{distance}=\sqrt{{\left({\mathrm{x}}_2-{\mathrm{x}}_1\right)}^2+{\left({\mathrm{y}}_2-{\mathrm{y}}_1\right)}^2} \\ \mathrm{Now},\mathrm{AB}=\sqrt{{\left(0-\mathrm{c}\right)}^2+{\left(-\mathrm{c}-0\right)}^2} \\ =\sqrt{{\mathrm{c}}^2+{\mathrm{c}}^2} \\ =\sqrt{2{\mathrm{c}}^2} \\ =\sqrt{2}\mathrm{c} \end{gathered}$$