Let A = (6,2) , and let B be the reflection of A over the line y=(1/2)x + 5. Find the coordinates of B.

Reflection matrix for y = 1/2*x + 5 applied to (6,2):

 

\(\begin{pmatrix} 3/5 & 4/5 \\ 4/5 & -3/5 \end{pmatrix} \begin{pmatrix} 6 \\ 2 \end{pmatrix} = \begin{pmatrix} 26/5 \\ 18/5 \end{pmatrix}\)

 

So the relfection is B = (26/5,18/5).