Correlation after opposite-sign linear transforms

Two random variables $X_1$, $X_2$ have correlation coefficient $0.2$. New variables are formed as $Y_1=2X_1+1$ and $Y_2=-4X_2+3$. Find the correlation coefficient of $Y_1$ and $Y_2$.

$-0.2$. Correlation ignores additive constants and positive scaling, but a negative scale factor flips its sign. The covariance picks up the product of slopes, $2\cdot(-4)=-8$, while the product of standard deviations picks up $2\cdot4=8$, so the ratio becomes $-0.2$.