Question

How do I write transformations? More specifically how would I show how a line is being shifted up and down and how can I show said line is being reflected?

Answer 1

Given an arbitrary line with gradient m, that passes through a point (x1, y1)

The equation of the line is

y - y1 = m( x - x1)

To shift the line up by g units

Then, the new equation becomes

y - y1 + g = m(x - x1)

To shift the line down by g units

Then, the new equation becomes

y - y1 - g = m(x - x1)

Taking the axis of reflection as x = 0

The reflection of the line is

-y - y1 = m( x - x1)

Taking the axis of reflection as y = 0

The reflection of the line is

y - y1 = m( -x - x1)