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### The translation of a Cartesian coordinate system displaces the origin.docx

1. The translation of a Cartesian coordinate system displaces the origin of the original coordinates (x, y) by a vector (dx, dy) to a new position in a new coordinate system (f, n). The transformation rule is given by x=f+dx y=n+dy Consider two vectors in the original coordinate system given by a = (a1,a2) and b = (b1 , b2). Show that the norm of a is not invariant under translation, but that the norm of the vector a Solution as the origin change a and b varies because they are calculated with respect to the origin but a-b is independent of placement of origin because it is not calculated with respect to origin but vectors a and b so vector a-b is invariant, and it will remain invariant in any other cartesian coordinates too normally, a-b = (a1-b1 , a2-b2) a=(f + da1 , n + da2) b=(f + db1 , n + db2)
2. a-b = ((f + da1) - (f + db1) , (n + da2 ) - (n + db2)) = (d(a1-b1) , d(a2-b2)) it is independent on f and n,that's what i was telling that they are invariant and does not depend on the change of origin
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