Question

If the origin is shifted to the point (0, -2) by a translation of the axes, the coordinates of a point become (3, 2). Find the original coordinates of the point.

Answer 1

Let the new origin be (h, k) = (0, -2) and (x, y) = (3, 2) 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 + 0 and 2 = Y + (-2)

⇒ X = 3 and Y = 4

Thus, the new coordinates are (3, 4)