Slide It, Stretch It, and the Correlation Does Not Move
A shift leaves every deviation from the mean untouched, and a stretch multiplies the covariance and one standard deviation by the same factor, so both cancel out of the ratio. The tempting answer of five times rho is worse than wrong: at rho = 0.40 it names 2.0, which Cauchy-Schwarz forbids any correlation from reaching. The article carries the general affine rule, the sign flip a negative factor produces, and the curved maps the invariance does not survive.