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Unformatted text preview: Math 466 — Homework Set 2 (8.10.2011) 1. P1 = Eand P2 = (222,92) be a pdir of phints in theihlane
and m the a line with equation ax + by + c = If éfm(P1) = am(P2)f.,—= Q2,'Where (321,93) and Q2 m (135,145), use; equations for? the
reﬂectiOn am to show that EPngi : |Q1Qg|. 3 ‘ ' ' 2. Let m be the line with an equation cm: + by ~+~ c = 0. Use the equations
for Um to show that 0mg = .5. 3. Show that if f E H then f is an isometry. 4. F121 in the missing entry in each row : Equation of ﬁne m 5. Let m be the line with an equation y = 2:1: — 5.
(a) Find the equations for the reﬂection in the line m.
(b) Find the images of (0,0), (1,—-3), (—2,?) and (2,4) under the
reﬂection in the line In. 6. If Q = TA.B(P) then without using the formulas for haifturns and . M, W
transiations Show that TAABO‘pTAy‘B w. 0Q. ‘7. Let A = (1,3), B = (5,1) and D =2 (0,0). Find the point C which is
uniqueiy determined by the equation TAB I 0360. 8. If P aé Q then show that THE, has infinite order. 9. Consider the foliowing ﬁgures.
(a) (If any) ﬁnd all lines of symmetry for each figure.
(13) (If any) ﬁnd ail points of symmetry for each ﬁgure.
(c) (If any) ﬁnd all possible rotational symmetries of each ﬁgure. maxi—urban}; Mountain... +1nwnuoi 3.303er Am<v ‘ Olav , all wnbcT-R Dengue: Nabcwax munch—ob :2 72.: (xi\ ".
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