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

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Solution

$\begin{matrix} L e t t h e t w o p o i n t s b e P (0, 0) a n d Q (36, 15) N o w, P Q = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} = \sqrt{{(36 - 0)}^{2} {(15 - 0)}^{2}} = \sqrt{{(36)}^{2} + {(15)}^{2}} = \sqrt{1296 + 225} = \sqrt{1521} = 39. N o w, I t i s g i v e n t h a t B i s l o c a t e d 36 k m e a s t a n d 15 k m n o r t h o f t o w n A . L e t u s t a k e A a s o r i g i n . N o w, A B = \sqrt{{(36 - 0)}^{2} + {(15 - 0)}^{2}} = \sqrt{12596 + 225} = \sqrt{1521} = 39. H e n c e, t h e d i s tan c e b e t w e e n t h e t w o t o w n s i s 39 k m . \end{matrix}$

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