Answer:
The dilation on any point of the rectangle is
.
Step-by-step explanation:
From Linear Algebra, we define the dilation of a point by means of the following definition:
(1)
Where:
- Coordinates of the point G, dimensionless.
- Center of dilation, dimensionless.
- Scale factor, dimensionless.
- Coordinates of the point G', dimensionless.
If we know that
,
and
, then scale factor is:
![(5,-5) = (0,0) +k\cdot [(2,-2)-(0,0)]](https://tex.z-dn.net/?f=%285%2C-5%29%20%3D%20%280%2C0%29%20%2Bk%5Ccdot%20%5B%282%2C-2%29-%280%2C0%29%5D)
![(5,-5) = (2\cdot k, -2\cdot k)](https://tex.z-dn.net/?f=%285%2C-5%29%20%3D%20%282%5Ccdot%20k%2C%20-2%5Ccdot%20k%29)
![k = \frac{5}{2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B5%7D%7B2%7D)
The dilation on any point of the rectangle is:
![P'(x,y) = (0,0) + \frac{5}{2}\cdot [P(x,y)-(0,0)]](https://tex.z-dn.net/?f=P%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%20%5Cfrac%7B5%7D%7B2%7D%5Ccdot%20%5BP%28x%2Cy%29-%280%2C0%29%5D)
(2)
The dilation on any point of the rectangle is
.