IB-tl . 



"'/;/,/ N 





EXERCISES 

 the AXM through an angle of 4.V, nd And the new eqt 



1 r + yt.ifl; 2. -*. 16; 3 v , 1, 



4 17x'- lOxy + 17y.m 



5 If tins axm are turned through the angle un-i', what does the 

 equation 4ry - 3x = o become? 



73. Transformation from rectangular to oblique axes, origin 

 inged. Let OX ami OK bo a given pair of rectangular 

 h-t OX 9 and OK' be 

 new axes makm- an an- 

 o> with t-ach MI)M i, and 

 angles XOX 1 and 

 be denoted 1 

 , respectively. Also 

 , any point in : 

 , have the coordinates 

 * and // \\ lion referred to the first pair of axes, and a/ and y* 



i referred to the second i 

 Draw ill,- ordinates JP, M 1 P, and QM', also draw M' R 



to thf r-a\ 

 Tli.n OM~O+M~ CM' 





sn 



simil.t: . | ' 

 li an- thf rr.jiiirr<l formulas of tran> >n from 



rectangular to oblique axes having the same origin. 



If o> = '.o, and consequently ^ = l0-f ^, thru formulas 



to [-JJ], and Ait. 7:J, therefore, include Art 

 a special case. 



By first solving fora/ and y\ formulas [-J.".] may also be 

 >yed to transform from oblique to rectangular axes. 



