Answer: (12,9), (6,9), (12,-6) and (6,-6)
Step-by-step explanation:
Given: The coordinates of the original rectangle are (8, 6), (4, 6), (8, −4), and (4, −4). We know that the coordinates of the image after dilation from the origin by a scale factor of k is given by:_
![(xy)\rightarrow(kx,ky)](https://tex.z-dn.net/?f=%28xy%29%5Crightarrow%28kx%2Cky%29)
Then, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are given by:_
(8, 6)→![(8\times1.5,6\times1.5)=(12,9)](https://tex.z-dn.net/?f=%288%5Ctimes1.5%2C6%5Ctimes1.5%29%3D%2812%2C9%29)
(4, 6)→![(4\times1.5,6\times1.5)=(6,9)](https://tex.z-dn.net/?f=%284%5Ctimes1.5%2C6%5Ctimes1.5%29%3D%286%2C9%29)
(8, −4) →![(8\times1.5,-4\times1.5)=(12,-6)](https://tex.z-dn.net/?f=%288%5Ctimes1.5%2C-4%5Ctimes1.5%29%3D%2812%2C-6%29)
(4, −4)→![(4\times1.5,-4\times1.5)=(6,-6)](https://tex.z-dn.net/?f=%284%5Ctimes1.5%2C-4%5Ctimes1.5%29%3D%286%2C-6%29)
Hence, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are (12,9), (6,9), (12,-6) and (6,-6).