If the origin is shifted to the point (1, 2) by a translation of the axes, find the new coordinates of the point (3, -4).

Question

Philoid · Accepted Answer

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)