19. Case study: Section formula

Exercise condition:

5 m.

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 $(1, 0)$, the ATM is located at $(6, 5)$, the temple is located at $(7, 6)$, and the hospital is located at $(9, 0)$. The coordinates are in kilometres.

[Note: Straight lines cover all the distances]

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

$(\frac{m x_{1} + n x_{2}}{m + n}, \frac{m y_{1} + n y_{2}}{m + n})$
$(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$
$(\frac{m x_{2} - n x_{1}}{m - n}, \frac{m y_{2} - n y_{1}}{m - n})$
$(\frac{m x_{2} - n x_{1}}{m + n}, \frac{m y_{2} - n y_{1}}{m + n})$

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

$(0, 5)$
$(5, 0)$
$(- 5, 0)$
$(0, - 5)$

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

$(4, 3)$
$(3, - 4)$
$(- 4, 3)$
$(3, 4)$

4. The distance between House and ATM:

$7.1 km$
$10.6 km$
$6.6 km$
$8.1 km$

5. Is the abscissa of house and hospital the different?

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