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:_
[tex](xy)\rightarrow(kx,ky)[/tex]
Then, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are given by:_
(8, 6)→[tex](8\times1.5,6\times1.5)=(12,9)[/tex]
(4, 6)→[tex](4\times1.5,6\times1.5)=(6,9)[/tex]
(8, −4) →[tex](8\times1.5,-4\times1.5)=(12,-6)[/tex]
(4, −4)→[tex](4\times1.5,-4\times1.5)=(6,-6)[/tex]
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).
