I am studying math for being a game developer and plan to code them once I finish the math and I wonder what’s the transformation matrix of a point about any arbitrary point. I studied this in college 5 years back, but I don’t have any notes of that time with me for some reason.

# Here’s how I’d derive for reflection of a point about the X-axis

(x,y)===>(x,-y)

The matrix required is obvious.

[1 0 ]

[0 -1]

But what about the transformations in an arbitrary line y=ax+b.

I try to analyze the stuffs above.

# Transformations through x-axis or about y=0.

We change the coordinates of y to negative.

# Transformations through y-axis or about x=0.

We change the coordinates of x to negative.

# But what will happen when I transform through y=ax+b.

What will happen here?