Two objects, A and B, are moving along two different straight lines at constant speeds. With reference to a particular coordinate system in which distance is measured in metres, the position of A at time t (in minutes) is(−2t+3,5t − 1), and the position of B is (2t+4,3t+7). ((a)) Find the equation of the line that A moves along. (b) Let d be the distance between A and B at time t. Show that an expression for ² in terms of t is given by d^{2}=20 t^{2}-24 t+65 (c) A student attempts to find the shortest distance between A and B as shown below. There are two lines where the working does not follow on from the previous line. Find and describe the two mistakes. Write out a correct solution.