Transformations of Axes - Practice Questions & MCQ

Transformations of Axes

Shifting of Origin

Point P has coordinate (x, y) in the original coordinate system, i.e. in xy-coordinate system.

If the new origin takes position as O’(h, k) with new x and y axes remaining parallel to old axes.

The coordinates of the point $P$ are now $(X, Y)=(x-h, y-k)$ w.r.t. the new coordinate system (i.e. $\left.Y^{\prime} O^{\prime} X^{\prime}\right)$.
Thus, $X=x-h$ and $Y=y-k$
Or, $x=X+h$ and $y=Y+k$
Note:
If the function $f(x, y)=0$ is with respect to original coordinate system, then the equation with respect to new coordinate system is $f(x+h, y+k)=0$.