In mathematics, i want to know the formular used to enlarge the shape

If the center of enlargement is the origin $(0,0)$, and the scale factor is $k$, then a point $(x,y)$ on the original shape is mapped to a new point $(x',y')$ on the enlarged shape using the formula:

$$(x', y') = (kx, ky)$$

If the center of enlargement is a point $(a,b)$ and the scale factor is $k$, then a point $(x,y)$ on the original shape is mapped to a new point $(x',y')$ on the enlarged shape using the formula:

$$(x', y') = (a + k(x-a), b + k(y-b))$$

Here, $k$ is the scale factor.

• If $k > 1$, the shape is enlarged.
• If $0 < k < 1$, the shape is reduced.
• If $k < 0$, the shape is enlarged or reduced and rotated by $180^\circ$.