Question

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. If the house is situated at $(2,4)$, bank at $(5,8),$ school at $(13,14)$ and office at $(13,26)$ and the coordinates are in kilometers?(Assume that all distances covered are in straight lines).

Answer 1

Given

House is situated at $H(2,4)$

Bank is situated at $B(5,8)$

School is situated at $S(13,14)$

Office is situated at $O(13,26)$

By distance formula

$HO=\sqrt{(13-2{)}^2+(26-4{)}^2}$

$HO=\sqrt{121+484}=\sqrt{605}$

$HO=24.59km$

$HB=\sqrt{(5-2{)}^2+(8-4{)}^2}$

$HB=\sqrt{9+16}=\sqrt{25}$

$HB=5km$

$BS=\sqrt{(13-5{)}^2+(14-8{)}^2}$

$BS=\sqrt{64+36}=\sqrt{100}$

$BS=10km$

$SO=\sqrt{(13-13{)}^2+(26-14{)}^2}$

$SO=\sqrt{144}$

$SO=12km$

Total distance travelled by Ayush is $=HB+BS+SO$

$Total=5+10+12=27km$

Distance between office and house is $24.59km$

Hence Extra distance $=27-24.59=2.41km$