Question

There is a man named Anand,who has worked hard and secured a

job in a multinational company. One day he started early to the

office. On the way he went to a ATM which is located at (5,8) to get

some money and then he went to his daughter’s school which is

located at(13,14) to pay the school fee of his daughter. Later he

reached the office which is located at (13,26) . If his house is located

at (2,4) and assuming that all the distances travelled in kilometers

and straight(linear) .

From the above data answer the following


ii)Find the distance from ATM to school?
​

Answer 1

Given:

• Anand secured a job in multi-national company.

• One day he started to the office from home and in-between, he visited some places whose coordinates are specified.
• Coordinates of Anand's house = $(2,4)$
• Coordinates of Anand's office = $(13,26)$
• Coordinates of Anand's daughter's school = $(13,14)$
• Coordinates of the ATM visited by Anand = $(5,8)$

To find:

The distance between ATM and Anand's daughter's school.

Formula to be used:

• It is mentioned that all the distances travelled are straight and are in kilometers.
• As the coordinates of the points visited by Anand are given, the distances between the required two points are calculated to find the distance between ATM and the school.
• Let the coordinates of ATM be denoted by $(x_1,y_1)$.
• Let the coordinates of the school be denoted by $(x_2,y_2)$.
• Now, the distance is calculated using the formula:

Distance between two points = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

Solution:

• Let the distance between ATM and school be denoted by "$d$".

⇒$d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$......(1)

• Using the given data and the equation (1), the distance between ATM and the school is calculated in the following manner:

$d=\sqrt{(13-5)^{2}+(14-8)^{2}}\\d=\sqrt{8^{2}+6^{2}}\\ d=\sqrt{64+36}\\ d=\sqrt{100}\\ d=10$

⇒The distance between ATM and school is $10Kilometers$.

Final Answer:

∴The distance between ATM visited by Anand and Anand's daughter's school is $10Kilometers$.