Answer:
Here, the coordinates of the given rectangle are (1,2), (3,2), (1,-1) and (3,-1)
In the dilation by the scale factor k with centered at origin,
![(x,y)\rightarrow (kx,ky)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28kx%2Cky%29)
Thus, If the dilation occurs by the scale factor of 2 with centered at origin,
New coordinates of the Rectangle are,
![(1,2)\rightarrow (2\times 1, 2\times 2)](https://tex.z-dn.net/?f=%281%2C2%29%5Crightarrow%20%282%5Ctimes%201%2C%202%5Ctimes%202%29)
![(3,2)\rightarrow (2\times 3, 2\times 2)](https://tex.z-dn.net/?f=%283%2C2%29%5Crightarrow%20%282%5Ctimes%203%2C%202%5Ctimes%202%29)
![(1,-1)\rightarrow (2\times 1, 2\times -1)](https://tex.z-dn.net/?f=%281%2C-1%29%5Crightarrow%20%282%5Ctimes%201%2C%202%5Ctimes%20-1%29)
![(3,-1)\rightarrow (2\times 3, 2\times -1)](https://tex.z-dn.net/?f=%283%2C-1%29%5Crightarrow%20%282%5Ctimes%203%2C%202%5Ctimes%20-1%29)
Thus, the coordinates of new rectangle are,
(2,4), (6,4), (2,-2) and (6,-2)