Question

A (0,0) B(6,3) ½ of the way from A to B

Answer 1

vectors

Answer 2

you can solve it without using vectors

Answer 3

if c be the center of AB
coordinates of C = ( 0+6/2 , 0+3 /2) = (3,1.5)
using distance finding formula we get AC=\[\sqrt{(3-0)^2 + (1.5-0 ) ^2}\]

Answer 4

3.354101966

Answer 5

in vectors you may write 3 i +1.5 j