Akash leaves home for school which is 12 km from his house. After the school, he goes to his club which is 7 km from his school. If his house, school and club all fall in a line, then what is the minimum distance he has to travel to get back home?

### Concept & 1D Coordinate Geometry When points lie on a single line, the distance between them is the absolute difference of their coordinates. To find the minimum return distance, arrange the points to minimize the span from the origin (house). ### Step-by-Step Solution * Let the house be at position 0 on a number line. * The school is at position 12 (since it is 12 km from the house). * The club is 7 km from the school, meaning its position can be either $12 + 7 = 19$ or $12 - 7 = 5$. * A position of 19 implies the club is further down the line, making the return trip back to 0 equal to 19 km. * A position of 5 implies the club lies directly between the house and the school, making the return trip equal to 5 km. * The minimum distance to travel back home from the club is therefore 5 km. ### Exam Strategy & Shortcut Simply subtract the two given distances: $12 - 7 = 5$. Since "minimum" is requested, you must assume the club lies directly on the return path between the school and the house. ### Common Pitfall Adding the distances to get 19 km, incorrectly assuming the school is always between the house and the club without considering other linear arrangements. ### Final Answer Therefore, the correct answer is **5 km**.