Math 532: Quiz 8, Spring 2011
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Name
(1) For each part below, the function f (x, y ) is dened as follows. First f rotates (x, y ) about the
point A = (1, 3) by /2 and then it takes the result and rotates it about the point B = (1, 1) by
. Thu
M AT H 5 32 , 7 36I : M ODER N GEOMETRY
Test 1 Solutions
Test 1 (2011):
Part I:
(1) Axioms for a finite AFFINE plane of order n
Axiom A1: There exist at least 4 distinct points no 3 of which are collinear.
Axiom A2: There exists at least 1 line with exact
M AT H 5 32 , 7 36I : M ODER N GEOMETRY
Test 2 Solutions
Test #2 (2011)
1) Theorems are listed on the last page of this test. They may or may not have the numbering
that you are accustomed to them having from class. Prove Theorem 2 using Theorem 1 (but
no
Math 532: Quiz 2
ANSWERS
Name
Axiom P1: There exist at least 4 points no 3 of which are collinear.
Axiom P2: There exists at least 1 line with exactly n + 1 (distinct) points on it.
Axiom P3: Given 2 distinct points, there is exactly 1 line that they both
M ATH 532, 736I: M ODERN G EOMETRY
Some Solutions to Old Final Exam Problems
Final Exam (1992):
Part II:
(2) (a) Let a, b, x, and y be such that B = (a, b) and A = (x, y ). Then
TB R,A = T(a,b) R,(x,y)
10a
cos() sin() x(1 cos() + y sin()
= 0 1 b sin() cos