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)
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