Math 466-HW-2 - Math 466 — Homework Set 2 (8.10.2011) 1....

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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\ ". '5‘ (NH ...
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Math 466-HW-2 - Math 466 — Homework Set 2 (8.10.2011) 1....

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