Answer:
The coordinates of the dillated vertices are
,
,
and
.
Step-by-step explanation:
From Linear Algebra, we define dilation by the following equation:
(1)
Where:
- Center of dilation, dimensionless.
- Original point, dimensionless.
- Scale factor, dimensionless.
- Dilated point, dimensionless.
If we know that
,
,
,
,
and
, then the dilated points are, respectively:
Point A
(2)
![A'(x,y) = (0,0) + 2\cdot [(1,1)-(0,0)]](https://tex.z-dn.net/?f=A%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%202%5Ccdot%20%5B%281%2C1%29-%280%2C0%29%5D)

Point B
(3)
![B'(x,y) = (0,0) + 2\cdot [(2,2)-(0,0)]](https://tex.z-dn.net/?f=B%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%202%5Ccdot%20%5B%282%2C2%29-%280%2C0%29%5D)

Point C
![C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)]](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BC%28x%2Cy%29-O%28x%2Cy%29%5D)
![C'(x,y) = (0,0) + 2\cdot [(4,1)-(0,0)]](https://tex.z-dn.net/?f=C%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%202%5Ccdot%20%5B%284%2C1%29-%280%2C0%29%5D)

Point D
![D'(x,y) = O(x,y) + k\cdot [D(x,y)-O(x,y)]](https://tex.z-dn.net/?f=D%27%28x%2Cy%29%20%3D%20O%28x%2Cy%29%20%2B%20k%5Ccdot%20%5BD%28x%2Cy%29-O%28x%2Cy%29%5D)
![D'(x,y) = (0,0) + 2\cdot [(2,-1)-(0,0)]](https://tex.z-dn.net/?f=D%27%28x%2Cy%29%20%3D%20%280%2C0%29%20%2B%202%5Ccdot%20%5B%282%2C-1%29-%280%2C0%29%5D)

The coordinates of the dillated vertices are
,
,
and
.