If the origin is shifted to the point
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.

Solution:

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 $y=Y+k$

$\Rightarrow 3=X+0$ and $2=Y+(-2)$

$\Rightarrow X=3$ and $Y=4$

Thus, the new coordinates are (3, 4)