Reflection over the line y = 3 followed by reflection over y= 8

Question

Directions: Given two reflections, determine a single transformation that could be used instead.

Reflection over the line y = 3 followed by reflection over y= 8

Answer 1

reflection over y = 3 is

f(x,y) = (x,6 - y)

reflection over y = 8 is g(x, y) = (x, 16 - y)

Then, g(f(x,y)) = g(x, 6 - y) = (x,16 - (6 - y)) = (x, y + 10)

The double reflection is equivalent to a shift up 10 or a vertical shift of 10.