Let $ \mathbf{R}(O, \theta) $ be the rotation with center $ O $ and angle $ \theta $ . Let $ \mathbf{H}(O, t) $ be the homothety with center $ O $ and coefficient $ t $ . Then the locus of $ Q $ is the image of $ \ell $ under $ \mathbf{R}(A, \alpha) \circ \mathbf{H}(A, \frac{1}{2\cos \alpha} ) $ and $ \mathbf{R}(A, -\alpha) \circ \mathbf{H}(A, \frac{1}{2\cos \alpha} ) $ .