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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 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 km

Solution:

Given, Ayush starts walking from his house to the office.

He goes to a bank first, from there to his daughter’s school and then reaches the office.

Given, the coordinates of house = (2, 4)

The coordinates of bank = (5, 8)

The coordinates of school = (13, 14)

The coordinates of office = (13, 26)

The coordinates are in km.

We have to find the extra distance travelled by Ayush in reaching his office assuming all distances covered are in straight lines.

The distance between two points P (x₁ , y₁) and Q (x₂ , y₂) is

√[(x₂ - x₁)² + (y₂ - y₁)²]

Distance between house(2, 4) and bank(5, 8) = √[(5 - 2)² + (8 - 4)²]

= √[(3)² + (4)²]

= √(9 + 16)

= √25

= 5 km

Distance between bank(5, 8) and school(13, 14) = √[(13 - 5)² + (14 - 8)²]

= √[(8)² + (6)²]

= √(64 + 36)

= √100

= 10 km

Distance between school(13, 14) and office(13, 26) = √[(13 - 13)² + (26 - 14)²]

= √[(0)² + (12)²]

= √(12)²

= 12 km

Distance travelled indirectly from house to office = 5 + 10 + 12 = 27 km

Distance between house(2, 4) and office(13, 26) = √[(13 - 2)² + (26 - 4)²]

= √[(11)² + (22)²]

= √(121 + 484)

= √605

= 24.59 km

Extra distance travelled by Ayush in reaching his office = 27 - 24.59 = 2.41 km

Therefore, the extra distance travelled by Ayush in reaching his office is 2.41 km.

✦ Try This: Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 meters × 80 meters. How much shorter is the route across the park than the route around its edges?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.4 Problem 6

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 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 km

Summary:

Ayush starts walking from his house to the 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.(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 km. The extra distance travelled by Ayush in reaching his office is 2.41 km

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