  In this article, we examine stretching and rotation of planar quasiconformal
mappings on a line. We show that for almost every point on the line, the set of
complex stretching exponents (describing stretching and rotation jointly) is
contained in the disk $ \overline{B}(1/(1-k^4),k^2/(1-k^4))$. This yields a
quadratic improvement over the known optimal estimate for general sets of
Hausdorff dimension $1$. Our proof is based on holomorphic motions and
estimates for dimensions of quasicircles. We also give a lower bound for the
dimension of the image of a $1$-dimensional subset of a line under a
quasiconformal mapping.
