# Find the distance between the pair of points (4, -1) and (-6, 3) . If necessary,

Find the distance between the pair of points (4, -1) and (-6, 3) . If necessary, express answers in simplified radical form and then round to two decimals places.

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Pohanginah
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: $$\displaystyle{d}=\sqrt{{{116}}}$$