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

avissidep 2021-09-18 Answered
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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Expert Answer

Pohanginah
Answered 2021-09-19 Author has 21438 answers
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: \(\displaystyle{d}=\sqrt{{{116}}}\)
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