Question

Transform $x-y+2=0$ to the parallel axes through the point $(-1,2)$

Answer 1

Let the co-ordinates $(x,y)$ of any point on the given line change to $(X,Y)$ on shifting the origin to the point $(-1,2)$, the new axes remaining parallel to the original axes.Then, we get

$x=X-1$ and $y=Y+2$

Substituting for $x=X-1$ and $y=Y+2$ we get

$(X-1)-(Y+2)+2=0$

$\Rightarrow X+1-Y-2+2=0$

$\Rightarrow X-Y+1=0$ is the required transformation.