# If the origin is shifted to the point

Question:

If the origin is shifted to the point (2, -1) by a translation of the axes, the coordinates of a point become (-3, 5). Find the origin coordinates of the point.

Solution:

Let the new origin be (h, k) = (2, -1) and (x, y) = (-3, 5) be the given point.

Let the new coordinates be (X, Y)

We use the transformation formula:

x = X + h and y = Y + k

$\Rightarrow-3=X+2$ and $5=Y+(-1)$

$\Rightarrow X=-5$ and $Y=6$

Thus, the new coordinates are (-5, 6)