Question

Transform $x-2y+3=0$ to the parallel axes through the point $(2,-5)$

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 $(2,-5)$, the new axes remaining parallel to the original axes.Then, we get

$x=X+2$ and $y=Y-5$

Substituting for $x=X+2$ and $y=Y-5$ we get

$(X+2)-2(Y-5)+3=0$

$\Rightarrow X+2-2Y+10+3=0$

$\Rightarrow X-2Y+15=0$ is the required transformation.