Let us find the distance between the pair of points

Given:

\(\displaystyle{\left({4},-{1}\right)}\) and \(\displaystyle{\left(-{6},{3}\right)}\)

Formula:

\(\displaystyle{d}=\sqrt{{{\left({x}_{{2}}-{x}_{{1}}\right)}^{{2}}+{\left({y}_{{2}}-{y}_{{1}}\right)}^{{2}}}}\)

\(\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}={\left({4},-{1}\right)}\)

\(\displaystyle{\left({x}_{{2}},{y}_{{2}}\right)}={\left(-{6},{3}\right)}\)

\(\displaystyle{d}=\sqrt{{{\left(-{6}-{4}\right)}^{{2}}+{\left(-{3}-{\left(-{1}\right)}\right)}^{{2}}}}\)

\(\displaystyle{d}=\sqrt{{{\left(-{10}\right)}^{{2}}+{\left({4}\right)}^{{2}}}}\)

\(\displaystyle=\sqrt{{{100}+{16}}}\)

\(\displaystyle{d}=\sqrt{{{116}}}\)

Answer: \(\displaystyle{d}=\sqrt{{{116}}}\)

Given:

\(\displaystyle{\left({4},-{1}\right)}\) and \(\displaystyle{\left(-{6},{3}\right)}\)

Formula:

\(\displaystyle{d}=\sqrt{{{\left({x}_{{2}}-{x}_{{1}}\right)}^{{2}}+{\left({y}_{{2}}-{y}_{{1}}\right)}^{{2}}}}\)

\(\displaystyle{\left({x}_{{1}},{y}_{{1}}\right)}={\left({4},-{1}\right)}\)

\(\displaystyle{\left({x}_{{2}},{y}_{{2}}\right)}={\left(-{6},{3}\right)}\)

\(\displaystyle{d}=\sqrt{{{\left(-{6}-{4}\right)}^{{2}}+{\left(-{3}-{\left(-{1}\right)}\right)}^{{2}}}}\)

\(\displaystyle{d}=\sqrt{{{\left(-{10}\right)}^{{2}}+{\left({4}\right)}^{{2}}}}\)

\(\displaystyle=\sqrt{{{100}+{16}}}\)

\(\displaystyle{d}=\sqrt{{{116}}}\)

Answer: \(\displaystyle{d}=\sqrt{{{116}}}\)