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 the 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 kilometers.

Given:

The house is situated at $(2, 4)$, bank at $(5, 8)$, school at $(13, 14)$ and office at $(13, 26)$.
To do:

We have to find the extra distance travelled by Ayush in reaching the office.

Solution:

We know that, Distance between two points $ \left(x_{1}, y_{1}\right) $ and $ \left(x_{2}, y_{2}\right) $
$ d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} $
The distance between house and bank $ =\sqrt{(5-2)^{2}+(8-4)^{2}} $
$ =\sqrt{(3)^{2}+(4)^{2}} $

$ =\sqrt{9+16} $

$ =\sqrt{25} $

$ =5 $
The distance between bank and daughter's school $ =\sqrt{(13-5)^{2}+(14-8)^{2}} $
$ =\sqrt{(8)^{2}+(6)^{2}} $
$ =\sqrt{64+36} $

$ =\sqrt{100} $

$ =10 $

The distance between daughter's school and office $ =\sqrt{(13-13)^{2}+(26-14)^{2}} $

$ =\sqrt{0+(12)^{2}} $

$ =12 $
The total distance travelled by Ayush $ =5+10+12=27 $ units

Distance between house to office $ =\sqrt{(13-2)^{2}+(26-4)^{2}} $
$ =\sqrt{(11)^{2}+(22)^{2}} $

$ =\sqrt{121+484} $
$ =\sqrt{605}=24.59 \approx 24.6 \mathrm{~km} $
Therefore, the extra distance travelled by Ayush in reaching his office $ =27-24.6=2.4 \mathrm{~km} $

Hence, the extra distance travelled by Ayush is $ 2.4 \mathrm{~km} $.

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Updated on: 10-Oct-2022

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