Expression 193: "p" Subscript, 10 , Baseline equals left parenthesis, 6 , negative 6 , right parenthesisp10=6,−6
193
angle of rotation
194
Expression 195: "a" Subscript, 10 , Baseline equals 0a10=0
195
transformed polygon (rotate, scale, and translate)
196
Expression 197: polygon left parenthesis, "p" Subscript, 10 , Baseline plus left parenthesis, "X" Subscript, "r" "o" "t" "a" "t" "e" 10 , Baseline left parenthesis, "T" Subscript, 10 , Baseline . "x" , "T" Subscript, 10 , Baseline . "y" , "a" Subscript, 10 , Baseline , right parenthesis , "Y" Subscript, "r" "o" "t" "a" "t" "e" 10 , Baseline left parenthesis, "T" Subscript, 10 , Baseline . "x" , "T" Subscript, 10 , Baseline . "y" , "a" Subscript, 10 , Baseline , right parenthesis , right parenthesis , right parenthesispolygonp10+Xrotate10T10.x,T10.y,a10,Yrotate10T10.x,T10.y,a10
197
rotation functions
198
Expression 199: "X" Subscript, "r" "o" "t" "a" "t" "e" 10 , Baseline left parenthesis, "x" , "y" , "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis equals "x" cosine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis minus "y" sine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesisXrotate10x,y,angle=xcosangle−ysinangle
199
Expression 200: "Y" Subscript, "r" "o" "t" "a" "t" "e" 10 , Baseline left parenthesis, "x" , "y" , "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis equals "x" sine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis plus "y" cosine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesisYrotate10x,y,angle=xsinangle+ycosangle
200
rotating point
201
Expression 202: left parenthesis, "p" Subscript, 10 , Baseline . "x" plus left parenthesis, distance left parenthesis, "p" Subscript, 10 , Baseline , "p" Subscript, 10 , Baseline plus "V" Subscript, 10 "a" , Baseline , right parenthesis , right parenthesis cos left parenthesis, "a" Subscript, 10 , Baseline plus "R" Subscript, 10 , Baseline , right parenthesis , "p" Subscript, 10 , Baseline . "y" plus left parenthesis, distance left parenthesis, "p" Subscript, 10 , Baseline , "p" Subscript, 10 , Baseline plus "V" Subscript, 10 "a" , Baseline , right parenthesis , right parenthesis sin left parenthesis, "a" Subscript, 10 , Baseline plus "R" Subscript, 10 , Baseline , right parenthesis , right parenthesisp10.x+distancep10,p10+V10acosa10+R10,p10.y+distancep10,p10+V10asina10+R10
202
Expression 203: "R" Subscript, 10 , Baseline equals 2 pi minus cosine to the negative 1st power left parenthesis, StartFraction, distance left parenthesis, "p" Subscript, 10 , Baseline , "p" Subscript, 10 , Baseline plus "V" Subscript, 10 "a" , Baseline , right parenthesis times left parenthesis, left parenthesis, "p" Subscript, 10 , Baseline . "x" plus "V" Subscript, 10 "a" , Baseline . "x" , right parenthesis minus "p" Subscript, 10 , Baseline . "x" , right parenthesis Over distance left parenthesis, "p" Subscript, 10 , Baseline , "p" Subscript, 10 , Baseline plus "V" Subscript, 10 "a" , Baseline , right parenthesis squared , EndFraction , right parenthesisR10=2π−cos−1distancep10,p10+V10a·p10.x+V10a.x−p10.xdistancep10,p10+V10a2
Expression 210: "V" Subscript, 11 "b" , Baseline equals left parenthesis, "x" Subscript, 11 , Baseline plus 5 , "y" Subscript, 11 , Baseline plus 17 , right parenthesisV11b=x11+5,y11+17
210
Expression 211: "V" Subscript, 11 "c" , Baseline equals left parenthesis, "x" Subscript, 11 , Baseline plus 17 , "y" Subscript, 11 , Baseline plus 12 , right parenthesisV11c=x11+17,y11+12
211
Expression 212: "V" Subscript, 11 "d" , Baseline equals left parenthesis, "x" Subscript, 11 , Baseline plus 12 , "y" Subscript, 11 , Baseline , right parenthesisV11d=x11+12,y11
212
point of rotation
213
Expression 214: "p" Subscript, 11 , Baseline equals left parenthesis, 8.5 , 8.5 , right parenthesisp11=8.5,8.5
214
angle of rotation
215
Expression 216: "a" Subscript, 11 , Baseline equals 0a11=0
216
transformed polygon (rotate, scale, and translate)
217
Expression 218: polygon left parenthesis, "p" Subscript, 11 , Baseline plus left parenthesis, "X" Subscript, "r" "o" "t" "a" "t" "e" 11 , Baseline left parenthesis, "T" Subscript, 11 , Baseline . "x" , "T" Subscript, 11 , Baseline . "y" , "a" Subscript, 11 , Baseline , right parenthesis , "Y" Subscript, "r" "o" "t" "a" "t" "e" 11 , Baseline left parenthesis, "T" Subscript, 11 , Baseline . "x" , "T" Subscript, 11 , Baseline . "y" , "a" Subscript, 11 , Baseline , right parenthesis , right parenthesis , right parenthesispolygonp11+Xrotate11T11.x,T11.y,a11,Yrotate11T11.x,T11.y,a11
218
rotation functions
219
Expression 220: "X" Subscript, "r" "o" "t" "a" "t" "e" 11 , Baseline left parenthesis, "x" , "y" , "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis equals "x" cosine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis minus "y" sine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesisXrotate11x,y,angle=xcosangle−ysinangle
220
Expression 221: "Y" Subscript, "r" "o" "t" "a" "t" "e" 11 , Baseline left parenthesis, "x" , "y" , "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis equals "x" sine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesis plus "y" cosine left parenthesis, "a" Subscript, "n" "g" "l" "e" , Baseline , right parenthesisYrotate11x,y,angle=xsinangle+ycosangle
221
rotating point
222
Expression 223: left parenthesis, "p" Subscript, 11 , Baseline . "x" plus left parenthesis, distance left parenthesis, "p" Subscript, 11 , Baseline , "p" Subscript, 11 , Baseline plus "V" Subscript, 11 "c" , Baseline , right parenthesis , right parenthesis cos left parenthesis, "a" Subscript, 11 , Baseline plus "R" Subscript, 11 , Baseline , right parenthesis , "p" Subscript, 11 , Baseline . "y" plus left parenthesis, distance left parenthesis, "p" Subscript, 11 , Baseline , "p" Subscript, 11 , Baseline plus "V" Subscript, 11 "c" , Baseline , right parenthesis , right parenthesis sin left parenthesis, "a" Subscript, 11 , Baseline plus "R" Subscript, 11 , Baseline , right parenthesis , right parenthesisp11.x+distancep11,p11+V11ccosa11+R11,p11.y+distancep11,p11+V11csina11+R11
223
Expression 224: "R" Subscript, 11 , Baseline equals cosine to the negative 1st power left parenthesis, StartFraction, distance left parenthesis, "p" Subscript, 11 , Baseline , "p" Subscript, 11 , Baseline plus "V" Subscript, 11 "c" , Baseline , right parenthesis times left parenthesis, left parenthesis, "p" Subscript, 11 , Baseline . "x" plus "V" Subscript, 11 "c" , Baseline . "x" , right parenthesis minus "p" Subscript, 11 , Baseline . "x" , right parenthesis Over distance left parenthesis, "p" Subscript, 11 , Baseline , "p" Subscript, 11 , Baseline plus "V" Subscript, 11 "c" , Baseline , right parenthesis squared , EndFraction , right parenthesisR11=cos−1distancep11,p11+V11c·p11.x+V11c.x−p11.xdistancep11,p11+V11c2
224
Frame 1
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225
"x" Subscript, 12 , Baselinex12
"y" Subscript, 12 , Baseliney12
negative 3−3
8.58.5
negative 3−3
negative 8.5−8.5
negative 20−20
negative 8.5−8.5
negative 20−20
8.58.5
226
Expression 227: polygon left parenthesis, "x" Subscript, 12 , Baseline , "y" Subscript, 12 , Baseline , right parenthesispolygonx12,y12
227
Expression 228: left parenthesis, negative 11.5 , 0 , right parenthesis−11.5,0
228
Frame 2
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229
"x" Subscript, 13 , Baselinex13
"y" Subscript, 13 , Baseliney13
1616
8.58.5
1616
negative 8.5−8.5
3333
negative 8.5−8.5
3333
8.58.5
230
Expression 231: polygon left parenthesis, "x" Subscript, 13 , Baseline , "y" Subscript, 13 , Baseline , right parenthesispolygonx13,y13
231
Expression 232: left parenthesis, 24.5 , 0 , right parenthesis24.5,0
