Question

Find the distance between the points $(0,0)$ and $(36,15)$. Can you now find the distance between the two towns $A$ and $B$ .

Answer 1

$\begin{array}{c}LetthetwopointsbeP\left(0,0\right)andQ\left(36,15\right)\\ Now,\\ PQ=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(36-0\right)}^2{\left(15-0\right)}^2}\\ =\sqrt{{\left(36\right)}^2+{\left(15\right)}^2}\\ =\sqrt{1296+225}\\ =\sqrt{1521}\\ =39.\\ Now,\\ ItisgiventhatBislocated36kmeastand15kmnorthoftownA.\\ LetustakeAasorigin.\\ Now,\\ AB=\sqrt{{\left(36-0\right)}^2+{\left(15-0\right)}^2}\\ =\sqrt{12596+225}\\ =\sqrt{1521}\\ =39.\\ Hence,thedis\tan cebetweenthetwotownsis39km.\end{array}$