Thread: coordinate geometry

does anybody know how to reflect a point over y=mx+b

Thanks

Originally Posted by anime_mania

does anybody know how to reflect a point over y=mx+b

Thanks

I'd have to give you a drawing to do this justice and I can't (I need a new scanner. I've been saying that for months now!)

Anyway, my whining aside, I'll give you a couple of ideas to work with.

It's easier to reflect over y = mx. So translate the point "b" units along the y- axis (down if b is positive, up if b is negative), reflect the point over y = mx, then translate the reflected point b units the other way along the y - axis.

Simple example:
Reflect the point (2, 3) over the line y = x - 1.

Translate (2, 3) 1 unit up along the y - axis: (2, 4).
Now reflect (2, 4) over y = x: (4, 2)
Finally, translate (4, 2) 1 unit down along the y - axis: (4, 1)

So reflecting the point (2, 3) over the line y = x - 1 gives the point (4, 1), as you can verify by graphing them directly.

-Dan

Originally Posted by anime_mania

does anybody know how to reflect a point over y=mx+b

Thanks

I presume you can a general formula?
I once tried to derive it but it got real messy and I stopped.