Science:Math Exam Resources/Courses/MATH152/April 2013/Question B 01 (b)/Hint 1

To reflect a vector about a line that goes through the origin, let $v=(v_{x},v_{y})$ be a vector in the direction of the line. The matrix which represents ${\text{Ref}}_{L}$ is given by

$\mathbf {A} ={\frac {1}{\lVert v\rVert ^{2}}}{\begin{bmatrix}v_{x}^{2}-v_{y}^{2}&2v_{x}v_{y}\\2v_{x}v_{y}&v_{y}^{2}-v_{x}^{2}\end{bmatrix}}$