# Strange question about reflection in Linear Algebra

Problem.

Apply b) or c) in exercise 26 to find the standard matrix of transformation for:

Reflection in the line $y= \sqrt{3x}$.

My solution

I start by pointing out that $y= \sqrt{3x}$ is not a line. Thereafter I ignore the directions and go for another method:

First I find the inverse of $y = \sqrt{3x}$ to be $y= \frac{x^2}{3}$. So to find the reflection, I want to map every $x$ value to $\frac{x^2}{2}$ and every $y$ value to $y$. Therefore $F \left( \begin{matrix} x\\y \end{matrix} \right) = \left( \begin{matrix} \frac{x^2}{3} \\ y \end{matrix} \right)$

...But I'm not sure if I'm doing the correct thing here. I may have misunderstood what is being asked? I'll let exercise 26 follow in case.

• I bet it was meant to be $y = \sqrt{3}\cdot x$, and either the typesetting was screwed up, or you misread. – Daniel Fischer Mar 12 '14 at 22:10
• I guess, it might be a typo somewhere: it is rather $$y=\sqrt3\,x\,.$$ – Berci Mar 12 '14 at 22:10
• Yeah guess it is. Can I still use my method? – Paze Mar 12 '14 at 22:11
• I notice my F is a bit off though, I Want to map every x value to a new y value but keep the x values the same. – Paze Mar 12 '14 at 22:11
• And would my method be correct if the question did read $y=\sqrt{3x}$ ? – Paze Mar 12 '14 at 22:13