19. Case study: Section formula

Ram went to a nearby hospital to be vaccinated. Rather than heading straight to the hospital, he first goes to an ATM, then to the temple, and the hospital. The house is located at \((2, 3)\), the ATM is located at \((6, 11)\), the temple is located at \((8, 11)\), and the hospital is located at \((10, 3)\). The coordinates are in kilometres.

 

[Note: Straight lines cover all the distances]

 

 

1. The formula for the line segment divided by a point internally:

 

2. The coordinates of a school, if it is located in the middle of a house and hospital:

 

3. The coordinates of a Museum, if it is one half of a distance from house to temple:

 

4. The distance between House and ATM:

 

5. Is the ordinate of house and hospital the same?