# At what point must the origin be shifted

Question:

At what point must the origin be shifted, if the coordinates of a point (-4,2) become (3, -2)?

Solution:

Let (h, k) be the point to which the origin is shifted. Then,

$x=-4, y=2, X=3$ and $Y=-2$

$\therefore \mathrm{x}=\mathrm{X}+\mathrm{h}$ and $\mathrm{y}=\mathrm{Y}+\mathrm{k}$

$\Rightarrow-4=3+h$ and $2=-2+k$

$\Rightarrow h=-7$ and $k=4$

Hence, the origin must be shifted to (-7, 4)