Question

ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of B after both reflections?

Answer 1

Reflections have a general rule, depending on which axis they are reflected on. Over the y axis (as indicated by x = 1) the formula is (-x,y). Over the x axis (as indicated by the line y = -3) the formula is (x,-y).

Answer 2

But those formulas are for x = 0 and y = 0. Since the lines are shifted, the transformation is too. Thus you can reflect the lines over x = 0 and y = 0 as well. Then add a value to shift the lines back to the ones you started with. Add shift the point reflected about both axes by the same amount.

Ex: Reflect the point (3,0) about x = 2.
Reflecting the line x = 2 over x = 0 will give you x = -2. To reflect the point over x = 0 will give you (-3,0). To shift the line back to x = 2, add 4. Thus to shift the point as well will give you (1,0).