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

(x, y) → (x, y + 2(3 -- y)) = (x, 6 - y) → (x, 6 - y + 2(8 - 6 + y)) = (x, y + 10);

Formula for reflection about line y = a: (x, y) → (x, 2a - y).

Then this you have to reflect about line y = b: (x, 2a - y) → (x, 2b - (2a - y)) = (x, 2b - 2a + y)