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Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughters school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at
(13, 26) and coordinates are in km
write answer in meter

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Solution

$L e t t h e c o - o r d i n a t e s o f t h e h o u s e b e H (x_{1}, y_{1}) = (2, 4), B a n k b e B (x_{2}, y_{2}) = (5, 8), t h e s c h o o l b e S (x_{3}, y_{3}) = (13, 14) & t h e o f f i c e b e O (x_{4}, y_{4}) = (13, 26) . A p p l y i n g t h e d i s t a n c e f o r m u l a . . . . . . . . . . . d = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} w e g e t H B = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(2 - 5)}^{2} + {(4 - 8)}^{2}} k m = 5 k m, B S = \sqrt{{(x_{2} - x_{3})}^{2} + {(y_{2} - y_{3})}^{2}} = \sqrt{{(5 - 13)}^{2} + {(8 - 14)}^{2}} k m = 10 k m, S O = \sqrt{{(x_{3} - x_{4})}^{2} + {(y_{3} - y_{4})}^{2}} = \sqrt{{(13 - 13)}^{2} + {(14 - 26)}^{2}} k m = 12 k m . ∴ T h e t o t a l d i s t a n c e c o v e r e d D = H B + B S + S O = (5 + 10 + 12) k m = 27 k m . T h e s t r a i g h t d i s t a n c e (d i s p l a c e m e n t) d = H O = \sqrt{{(x_{1} - x_{4})}^{2} + {(y_{1} - y_{4})}^{2}} = \sqrt{{(2 - 13)}^{2} + {(4 - 26)}^{2}} k m = 24.6 k m . S o t h e e x t r a d i s t a n c e t r a v e l l e d b y A y u s h i s D - d = (27 - 24.6) k m = 2.4 k m . A n s - T h e e x t r a d i s t a n c e t r a v e l l e d b y A y u s h i s 2.4 k m .$

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