Find the new coordinates of point (3, –4) if the origin is shifted to (1, 2) by a translation.

Coordinates of the new origin are h = 1, k = 2.

Original coordinates are x = 3, y = -4.

Transformation relations:

x = x' + h   i.e.,   x' = x - h

y = y' + k   i.e.,   y' = y - k

Substituting values:

x' = 3 - 1 = 2

y' = -4 - 2 = -6

Therefore, the coordinates of the point (3, -4) in the new system are (2, -6).