Notice that the distribution of the vertices of the figure is the same, in other words,
B' is in 'the same position' with respect to A' and C' as B is with respect to A and C.
Therefore, neither reflection nor rotation can be the answer.
Thus, the answer is translation, option C
the equations are already in slope-intercept form, therefore
so their slopes are 2 and 4.
parallel lines have exactly the same slope, these ones do not, so they're not parallel.
perpendicular lines, have negative reciprocal slopes, in short, their product gives -1, 2*4 ≠ -1, so they're not perpendicular either.