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

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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falhiblesw
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