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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
Solution
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.