Question

Transform $x-3y+5=0$ 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

$(X+1)-3(Y+2)+5=0$

$\Rightarrow X+1-3Y-6+5=0$

$\Rightarrow X-3Y=0$ is the required transformation.