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# wsol1 - Math 2163 Jeff Mermin’s sections Written project...

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Unformatted text preview: Math 2163 Jeff Mermin’s sections, Written project 1, due September 16 Write up all work neatly in complete mathematical sentences. Make intelligent use of whitespace. 1. Let P = (a, b), Q 2 (ad), and R = (e, f) be any three points in R2. Use vectors and the cross product to ﬁnd a formula, in terms of a, b, c, d, e, and f, fer the areg oi ttiengle PQR. Sold’l‘|';/:i CHFI'S‘l'lCA Saijcr" AVQOKZ x Al : < 0 j 0 )(e-«WM-(Wm Am M?” H A) \ Wm (M We (Mb? ., ' IX X ﬂl \ ' ,. V 1 cot ’ ,. r H x \ (Mil AV 2 Avw '* z @ol’aobehw'o‘ﬂc—hc—Aw Swim cvo'ﬂ Vvoolﬂé'l culug PK ; X I<é,a Noam. {mice Wk v we wi\\ AWE: at ﬁwb 9&1 ‘j Km, 0H». +0 m Meow-3‘6“ (c-ok) 'l" 'b I O > ,,S£:5;4;LQ:_ LIZEWI Ava/KP: (ole’aot’cb‘wipt bc+493 2. Consfezrjthe 47x 2 matrix M forméd’bﬁmmord’inates of P, Q, a b c d e f a b the “sum of the downward diagonals” and U = cb + ed + a f be the “sum of the upward diagonals”. Find a formula for the area of triangle PQR in terms of D and U. Salu‘l'lw‘ \77 "THEoﬁorA (,EISEL“: R, and P on top of each other, M = . Let D = ad + cf + eb be \ Amt ': C’Q‘ Cb “an «mtg 4,696 .Mwﬂ. (Prawn a“) Q -_- ¢9vr __ W> sulphur ‘, L a v «aw-ram cm} 1““- \ Aew My. AR?) 3? com/Q»! ~ Veg rr m‘wx‘r- if}; .{ I; {.mdey. C r-On( C}: K.) {N}, ‘ dd in “1": 5 'l (,Qléakﬁhﬁﬁ C F545;) Prod“: VF . A mom sendad “won by /( Owen Gwm'cu”: SUPPOSQ’ M -. ﬂ {TY Pain 1"; P) Q 3 x ’ (xx/“‘4‘; Eﬂ'aC‘KPC‘ 57"“- C j k Cm” “AWAY. TVUM D (Ad 1 a? 1‘ {+11 95 or "dc-g- w: A (:licwr'i‘xwrii’ﬁ OH 0\ U = (Ah + (71“? * ed -+ (1b for ‘ u 9 6.. ‘ § “upwm d ﬂimsy/wk“, “I my; {0st A W " P‘004V‘ 1 LH .PW {41173321}, Q ‘-' (Cm‘f) , Q: {£37 1), Cuici COUSSCU‘V 4AM M xawqui Pﬁ- Eﬁ'. (ma VZR‘Q 19v mm quad PQQS. 8mm Am T 195\$ \ Wm Cweu «>4; ad is + bljld/U '1 “2, WWW h = PG , \n.‘ PP, b1:- P‘Zx am by PS2. Tthre un " PS) “PG y yo Cf - Cb - a? ed 1 ad ‘1' 9‘0 ch-eb —C\\’\ —3¥ -Cnc +3b ((7 + ed 1030) (6&1) 3 cmd I! 4. Find the area of the pentagon with vertices (0, 0), (1, l), (2, 4), (3, 9), and ‘ (4,16). SoLfHW‘ ‘97 V;k.+0(ic\ Hap-1’: 1V? w 'Q ‘4 ‘1‘}: w‘ 1;" g4" 2‘ r7 p1 1;"?Wnﬁié “’ a g , - IQ'SD _ i? U T O“: ¥ '*' 35!.) ‘v I: M" -_ 2133:: a a », .3, » 1 A“ _ .' [ 3,2 In ..., C a ‘1 é ‘ —- ﬂ.” * u M :41 1 L - 3,. ex L: '7'. Z / 51 L 4* . . g? y g , Ni. , ».;’—- (Weigaﬂa 1mm ago .2 .q "’é’ﬂ’z‘j? 1"" --: 47‘ -,.3 fix, . A'. W 1- w. a“, ‘ _. . . . 3 ’1' h" 1 .1 :4: V 2, ,1; 7/6- 3» 444 .v - £2 ...
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