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 ? (Assume that all distance covered are in straight lines). If the house is situated at (2, 4) , bank at (2, 4), bank at (5, 8) school at (13, 14) and office at (13, 26) and co-ordinates are in km.

Explanation

Consider the co-ordinates of house, H(2, 4), bank, B(5, 8), school, S(13, 14) and office, O(13, 26).
`" ""Distance "HB^(2)=(5-2)^(2)+(8-4)^(2)=3^(2)+4^(2)=9+16=25`
`rArr" "HB=5" km"`
`" "` Distance `BS^(2)=(13-5)^(2)+(14-8)^(2)=8^(2)+6^(2)=64+36`
`rArr" "BS^(2)=100`
`rArr" "BS=10" km"`
Distance `" "SO^(2)=(13-13)^(2)+(26-14)^(2)=0^(2)+12^(2)=12^(2)`
`rArr" "SO=12" km"`
Total distance travelled by Ayush from house to bank to school and then to office
`" "=HB+BS+SO=5+10+12=27" km"`
Direct distance from house to office =HO
`rArr" "HO^(2)=(13-2)^(2)+(26-4)^(2)=(11)^(2)+(22)^(2)`
`rArr" "HO^(2)=121+484`
`rArr" "HO=sqrt(605)=24.6" km"`
So, extra distance travelled by Ayush = 27 km- 24.6 km = 2.4 km.
Hence, extra distance travelled by Ayush = 2.4 km.