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

This question is due very soon so it would be appreciated if you could help!

Jul 28, 2020
edited by Guest  Jul 28, 2020

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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).

Aug 2, 2020