# Homework Help: Reflection of a vector

1. May 2, 2015

### fattycakez

1. The problem statement, all variables and given/known data
Find the (exact) reflection of the vector v = (5, 1) across the line: y = 2x.
Hint: A sketch of v and the line may suggest an approach.

2. Relevant equations

3. The attempt at a solution
I found the matrix
-3/5 6/5
4/5 2/5
which seems like it gives the reflection across y=2x

But my question is: is there way to do this by rotating the axes and changing bases? (I'm pretty sure this is what the assignment is asking me to do)
I'm having a hard time visualizing it since no angle is given to put into the rotation equations for R2
i.e.
x'=xcosθ +ysinθ
y'=-xsinθ+ycosθ

Any help is greatly appreciated :)

2. May 2, 2015

### SammyS

Staff Emeritus
What angle does the vector, <5, 1>, make with the line y = 2x ?

3. May 2, 2015

### fattycakez

Man I'm slow, it makes an angle of 52.125! When I use that and the (5,1) in the rotation equations it looks like its reflecting in the wrong direction
The new vector appears to be at a 90 degree angle with y=2x, do I need another rotation or something like that?
Thanks :)