Why in transformation with Matrices they only give you reflection formulas for the x,y and y=x formula?

Question

What if you want to reflect it over another line?
math experts or people that really know there math answer this question....

Answer 1

You must be in an elementary class. It is possible to reflect across any line. You essentially project the vector down to the reflection line, then get the perpendicular component and the reflection has the same component along the line but the opposite sign for the perpendicular component.

If you're really interested I'd have to do a little more work to show you.

May not,

Say you line of reflection is given by the vector R=(1, 5) [ can you see that this is the line y=5x ?]

the component of an arbitrary vector along the line is the dot product:

vl = v dot R, the perpendicular component is vp=v-vl, right?

So the reflected vector is:

Vr = vl +(-vp)

So, Vr is the reflection of v across the line y=5x, also denoted by its vector (1,5)

ta da.