Question

Find the distance of the point (6,-8) from the origin. Also find the midpoint of the line joining these two points.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{P}\left(6,-8\right)\mathrm{be}\mathrm{the}\mathrm{given}\mathrm{point}\mathrm{and}\mathrm{O}\left(0,0\right)\mathrm{be}\mathrm{the}\mathrm{origin}. \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{points}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\mathrm{and}\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)\mathrm{is} \\ \mathrm{Now},\mathrm{using}\mathrm{distance}\mathrm{formula}: \\ \mathrm{OP}=\sqrt{{\left(0-6\right)}^2+{\left(0+8\right)}^2} \\ \Rightarrow \mathrm{OP}=\sqrt{36+64} \\ \Rightarrow \mathrm{OP}=\sqrt{100} \\ \Rightarrow \mathrm{OP}=10\mathrm{units} \\ \mathrm{Now},\mathrm{coordinates}\mathrm{of}\mathrm{mid}\mathrm{point}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{segment}\mathrm{joining}\mathrm{the}\mathrm{points}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\mathrm{and}\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)\mathrm{is}\left(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}\right) \\ \mathrm{Now},\mathrm{coordinates}\mathrm{of}\mathrm{mid}\mathrm{point}\mathrm{of}\mathrm{line}\mathrm{segment}\mathrm{joining}\mathrm{P}\left(6,-8\right)\mathrm{and}\mathrm{O}\left(0,0\right)\mathrm{is}\left(\frac{6+0}{2},\frac{-8+0}{2}\right)=\left(3,-4\right) \end{gathered}$$