Question:
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).
Solution:
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 $y=Y+k$
$\Rightarrow 3=X+1$ and $-4=Y+2$
$\Rightarrow X=2$ and $Y=-6$
Thus, the new coordinates are $(2,-6)$