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)
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