Consider the points P = (8,1), P = (-4,7), P3=(2, 6), P4 = (6,4), and P5 =(4,-9) of the plane. (i) For all i, j = 1, 2, ..., 5, find the distance di, between the points P and Pj. Show your work by creating the matrix D = ||dj|| whose entries are the numbers dij rounded to two decimal places. (ii) Consider then the relation R on the set A = {P, P2, P3, P4, P5} defined by (P, Pj) R dj = dist(P, Pj) < 8, and find the matrix MR of the relation R. (iii) Use (i) to determine whether the relation R is: (a) reflexive, (b) symmetric, (c) transitive, (d) an equivalence relation on A. (iv) If R is an equivalence relation, find the corresponding equivalence classes.