Question

12 points for!

A figure in the coordinate plane is reflected across the line y= x+2 and then across the line y= x+4. What is the translation vector that describes the composition of the reflections?

Answer 1

(x, y) ⇒ (x -2, y +2)

Explanation:

Reflection across the line y = x+2 has the effect of interchanging x and y and translating by (-2, 2).

Reflection across the line y = x+4 has the effect of interchanging x and y and translating by (-4, 4).

The composition of these transformations is then ...

(x, y) ⇒ ((x +2) -4, (y -2) +4) = (x -2, y +2)