If the origin is

Let the new origin be (h, k) = (1, 2) and (x, y) = (3, -4) be the given point.

Let the new coordinates be (X, Y)

We use the transformation formula:

x = X + h and y = Y + k

⇒ 3 = X + 1 and -4 = Y + 2

⇒ X = 2 and Y = -6

Thus, the new coordinates are (2, -6)