A straight jogging track begins at S(−5, 4) and ends at U(10, −6).
(i) A water station T is to be placed on the track so that ST : TU = 2 : 3. Find the coordinates of T.
(ii) A resting bench V will be installed on the extension of the track beyond U such that UV equals TU and V lies on the same straight line as S, T and U, with U between T and V. Determine the coordinates of V.
(iii) Show, by calculating and comparing suitable pairs of distances, that S, T, U and V are collinear.