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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?

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sqdancefan

Answer:

  (x, y) ⇒ (x -2, y +2)

Step-by-step 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)

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