Question

A figure in the coordinate plane is reflected across the line y = x + 1 and then across the line y = x + 3. Find a translation vector that is equivalent to the composition of the reflections. Write the vector in component form.

I know the answer is (-2, 2), but how?

Answer 1

well, look at what happens to point (-1,0)
it remains at (-1,0) when reflected around y=x+1 because it is on that line
so just reflect it about y = x+3
drawing the graph I see it went left 2 from -1 and up the same amount, 2, from 0
so left 2 and up 2 :)

Answer 2

So if (0, 0) was reflected over y = x + 1, then would the vector be (-1, 1)? This isn't exactly related to the above question, but just wanted to check.

Thanks!