Is there even a multiplier?

Question

673. Decide whether the transformation T (x, y) = (4x − 3y, 3x + 4y) is a similarity transfor- mation. If so, what is the multiplier m?

Answer 1

say x=OPx'cos(ß)-OPy'sin(ß),,,,ß positive rotation of point around origin

y=OPx'sin(ß)+OPy'cos(ß)

if A=OPcos(ß)=4,,,,B=-OPsin(ß)=-3 ,,, from x equation

then OP=√(A²+B²)=5

ß=tan^-1(3/4)

same with y, C=OPsin(ß)=3,,, D=OPcos(ß)=4

figures are rotated around origin (correction) and have multiplier of 5

similarity is maintained