Along a straight deserted highway stands a lamppost L. Van A is parked 300m west of the lamppost, van B is 120m east of the lamppost, and van C is 200m west of van A. All distances are measured along the same straight line.
(i) Taking the lamppost L as origin (x=0) and choosing east as the positive direction, state the positions of vans A, B and C (include sign and unit).
(ii) Now select van C as the origin while retaining east as the positive direction. Determine the positions of lamppost L, van A and van B relative to this new reference point.
(iii) Prove, using the numerical values obtained above, that the algebraic difference between the positions of any two vans remains the same regardless of whether L or C is chosen as the reference point. Generalise your reasoning for any pair of points placed along a straight line.