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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 daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office?

Ayush starts walking from his house to the office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s 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.

Answers (1)

The given point are (2, 4), (5, 8), (13, 14), (13, 26)
  Distance between house and bank

= \sqrt{\left ( x_{2}-x_{1} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}}
 = \sqrt{\left ( 5-2 \right )^{2}+\left ( 8-4 \right )^{2}}= \sqrt{9+16}= 5
Distance between bank and school
= \sqrt{\left ( 13-5 \right )^{2}+\left ( 14-8 \right )^{2}}= \sqrt{64+36}= \sqrt{100}= 10
Distance between school and office
= \sqrt{\left ( 13-13 \right )^{2}+\left ( 26-14 \right )^{2}}= \sqrt{\left ( 12 \right )^{2}}= 12
Distance between office and house
= \sqrt{\left ( 13-2 \right )^{2}+\left ( 26-14 \right )^{2}}
= \sqrt{121+484}
= \sqrt{605}
= 24\cdot 59

Total distance covered from house to bank, bank to school, school to office = 5 + 10 + 12 = 27
Extra distance covered = 27 – 24.59 = 2.41 km.

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