The new co-ordinates of a point $(4,5)$ when the origin is shifted to the point $(1,-2)$ are:
$1$. $(5,3)$
$2$. $(3,5)$
$3$. $(3,7)$
$4$. None.
My Attempt:
$$\#1$$ The origin is shifted to the right by $1$unit (right means positive $x$). The point is thus shifted identically, thus the first coordinate of your new point is $5$.
The origin is also shifted down by $2$ units (down means negative $y$). The point goes similarly, so the second coordinate is $3$.
Result is, thus, $(5, 3)$.
$$\#2$$
Let the new origin be $(h,k)=(1,-2)$ and $(x,y)=(4,5)$ be the given point.
Therefore the new co-ordinates $(X,Y)$
$$x=X+h$$ $$4=X+1$$ $$X=3$$
$$y=Y+k$$ $$5=Y-2$$ $$Y=7$$
So, the result is $(X,Y)=(3,7)$.
I got two different answers. Which one is correct?