Enlargement-how to enlarge a shape by negative scale factor
The diagram shows a shaded shape. Enlarge the shaded shape by scale factor $\frac{-1}{2}$ with centre of enlargement of $(-1,0)$.
Hi could someone tell me how I would do this please I'm very confused on how to enlarge this shape by negative half scale factor. Does it become flipped?
$\endgroup$1 Answer
$\begingroup$If I understand correctly, you have to make an homothetic transformation.
If $A$ is the center of your homothetic transformation (here, $(-1,0)$) and $k$ your homothetic factor (here, $-1/2$), the image of the point $X$ is $X'$ such that it verifies the following equation:
$$k\vec{AX}=\vec{AX'}$$
So, here, you have to calculate $k\vec{AX}$ for each vertex $X$ of your shape. And it will give:
Basically, if you want to construct the image of $X=(x,y)$ by an homothetic transformation of center $A=(a,b)$ and factor $k$, you have to do the following:
- Draw the line $AX$
- Calculate the distance $|AX|$ (using their respective coordinates). This distance is $|AX|=\sqrt{(x-a)^{2}+(y-b)^{2}}$.
- If $k$ is positive, draw a vector on the line $AX$ going from $A$ to the same side of $X$ and of length $k|AX|$. You have now the image $X'$ of $X$. If $k$ is negative, draw a vector on the line $AX$ going from $A$ to the opposite side of $X$ and of length $|k||AX|$. You now have the image $X'$ of $X$.
