To find the distance between her home and her latest position:
According to the question, the diagram is,
Consider the right triangle,
AB=120 km
BC=50 km
To find AC:
Using Pythagoras theorem,

Hence, the distance between the new position and her home is 130 km.
For a survey like this, you want to take a random sample. It would be a good idea to use an alphabetical list of the students. Then, you could randomly select students from the list.
The principal would want to avoid surveying all the same type of students. For example, don't just ask the athletes.
Well since you're using 3/8 and you need to make 4 batches, you need to multiply 3/8 with 4 it would equal 12/8 or 1 4/8 (I could be wrong but this is my answer hopefully this helps) :) <span />