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 ? ( 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 .

Answer 1

The position of the ayush's house is (2, 4) and that of the bank is (5, 8).
The distance between the house and the bank is
$$\begin{gathered} d_1=\sqrt{{\left(5-2\right)}^2+{\left(8-4\right)}^2} \\ =\sqrt{3^2+4^2} \\ =\sqrt{9+16} \\ =5units \end{gathered}$$
The position of the the bank is (5, 8) and that of the school is (13, 14).
The distance between the bank and the school is
$$\begin{gathered} d_2=\sqrt{{\left(13-5\right)}^2+{\left(14-8\right)}^2} \\ =\sqrt{8^2+6^2} \\ =\sqrt{64+36} \\ =10units \end{gathered}$$
The position of the school is (13, 14) and that of the office is (13, 6)
The distance between the bank and the school is
$$\begin{gathered} d_3=\sqrt{{\left(13-13\right)}^2+{\left(26-14\right)}^2} \\ =\sqrt{0^2+{12}^2} \\ =12units \end{gathered}$$
Suppose d be the total distance travelled by ayush
$$\begin{gathered} d=d_1+d_2+d_3 \\ d=5+10+12 \\ d=27km \end{gathered}$$
Now, let D be the shortest distance between ayush house and the office,
$$\begin{gathered} D=\sqrt{{\left(13-2\right)}^2+{\left(26-4\right)}^2} \\ =\sqrt{{11}^2+{22}^2} \\ =\sqrt{605} \\ =24.6km \end{gathered}$$

Thus the extra distance covered by ayush is d − D = 27 − 24.6 = 2.4 km.