Two triangles is mapped using the rules (x, y)→(−x, y) followed by (x, y)→(x−1, y+2)
which statement describes the relationship between the two triangles?
( see attachment)

Well (x, y)→(−x, y) means it's reflected off the y-axis(You can experiment this with random points on a graph)
(x, y)→(x−1, y+2) means that every point is moved to the left by 1 and up by 2, in other words, the triangle is translated left 1 up 2.
Since the only thing that effects congruency is dilation(rotation, translation, and reflection only move the shape, not change it), The new triangle should equal the old one.
Thus we would get the first choice