

\*rOBM i ? C06KDIXA T* 



which are the equation* (or formula*) of transformation 

 from any given axes to new axes which are respectively 

 parallel i.. the original ones, the new origin being the point 

 (Xa(A, *). These formulas, moreover, are independent 



10 angle between the axes. 



As a simple ill u of the usefulness* of such a change 



Oft, Mipiiote the equation 



*- >v - Sty -rf -*-** . . (1) 



given, in which s and y are coordinates referred to the axes 



M.I OY. 

 Now let Pm (*, y) be any point on the locus LJj of this 



equation. ami 1* t < /. ,/' ) )>< the coordinates of the same 

 ' when it is referred to the axes O'X 1 and O Y 1 ; 



ar-x'-fA and y = y' + k. 



:ut ing these values in the given equation for the 



w and y there invol .-.punon in y and y' is obtained 



which is satisfied by the coordinates of every point on Z,L, 



it is the equation of the same locus. The substitution 



gives: 



r *) - 2 A<>' + A) + <y 4- *) - 2 *(y' + *)-<!*- A^-H 



)i reduces to 



*" + y' a = 



a much simpler equation than < 1 . i>m representing the 

 same locus, merely referred to other 



EXERCISES 



1. What u the equation fur the locos of 3x - 2y = 6, if the origin 

 be changed to the point (4, 3), directions of axes unchanged ? 



2 \\:..ii does the equation x + 5* - 4* - y = 18 become if the 

 origin be changed to the point (2, 3), directions of axes unchanged? 



