A rugby player throws the ball from point A that is 18 yards from the

Khadija Wells 2021-08-18 Answered
A rugby player throws the ball from point A that is 18 yards from the endline and 12 m from the sideline (12,18). The ball lands at point B that is is 42 yards from the same endline and 50 yards from the same sideline. How long was the throw?

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Expert Answer

falhiblesw
Answered 2021-08-19 Author has 18293 answers
To find the distance, use the distance formula:
\(\displaystyle{d}=\sqrt{{{\left({\underset{{{2}}}{{{x}}}}-{\underset{{{1}}}{{{x}}}}\right)}^{{2}}+{\left({\underset{{{2}}}{{{y}}}}-{\underset{{{1}}}{{{y}}}}\right)}^{{2}}}}\)
From the given \(\displaystyle{\left({\underset{{{1}}}{{{x}}}},{\underset{{{1}}}{{{y}}}}\right)}={\left({12},{18}\right)}{\quad\text{and}\quad}{\left({\underset{{{2}}}{{{x}}}},{\underset{{{2}}}{{{y}}}}\right)}={\left({50},{42}\right)}\). Substitute:
\(\displaystyle{d}=\sqrt{{{\left({50}-{12}\right)}^{{2}}+{\left({42}-{18}\right)}^{{2}}}}\)
\(\displaystyle{d}=\sqrt{{{\left({38}\right)}^{{2}}+{\left({24}\right)}^{{2}}}}\)
\(\displaystyle{d}=\sqrt{{{1444}+{576}}}\)
\(\displaystyle{d}=\sqrt{{2020}}\)
\(\displaystyle{d}\approx{44.9}\) m
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