Question:
If the origin is shifted to the point (-3, -2) by a translation of the axes, find the new coordinates of the point (3, -5).
Solution:
Let the new origin be (h, k) = (-3, -2) 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 $y=Y+k$
$\Rightarrow 3=X-3$ and $-5=Y-2$
$\Rightarrow X=6$ and $Y=-3$
Thus, the new coordinates are (6, -3)
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