ok , let me start from the meaning of word translation .
translation means moving an object by a certain distance in any direction.
the nature of the object i.e shape, size does not change. neither the figure is
reflected, nor rotated.
as δ abc is translated, it is not given it is translated in which direction
so,(2,-7) lies in fourth quadrant.
if translation of t units is applied to the coordinates of b (2,-7) i.e x in right direction,and y in up then new coordinates, b'=(2+t, -7+t)
if translation of t units is applied to the coordinates of b(2,-7) i.e x in right direction,and y in down then new coordinates, b'=(2+t, -7-t)
if translation of t units is applied to the coordinates of b(2,-7) i.e x in left direction,and y in up then new coordinates, b'=(2-t, -7+t)
if translation of t units is applied to the coordinates of b(2,-7) i.e x in left direction,and y in down then new coordinates, b'=(2-t, -7-t)