To emphasize that we are thinking of it as the Eucliden plane we will denote it by E2. The point of E2 are the elements of E2, the lines are subsets of E2 of the form. Here are two questions.

6 to emphasize that we are thinking of it as the Euclidean plane we will denote it by E2. The points of E2 are the elements of E2, the lines are subsets of E2 of the form {(x, y) EE? | ax + by + c = 0} with a2 + 62 + 0 (why do we require a2 + 62 + 0?), two lines e(a, b, c) and e(a', b', c ) that intersect at a point p meet at a right angle at p provided that aa' = -bb', and the distance between two points p = (p1, p2) and q = (91, q2) in E2 is given by6 dist(p, q) = (p1 - 91)2 + (p2 - q2)2. Of the five axioms, only I, IV, and V require verification. (a) Show axiom I holds in E2; that is, suppose p = (P1, p2) and q = (q1, q2) are two distinct points in E2 and show that there is a line & that contains p and q. (b) Show that the line in (19a) is unique. R is a reflexive relation on X such that for all x, y, z E X, if xRy and yRz, then zRx