Question

A rectangle has vertices (8, 6), (4, 6), (8, −4), and (4, −4). What are the coordinates after dilating from the origin by a scale factor of 1.5?

Answer 1

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:_

$(xy)\rightarrow(kx,ky)$

Then, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are given by:_

(8, 6)→$(8\times1.5,6\times1.5)=(12,9)$

(4, 6)→$(4\times1.5,6\times1.5)=(6,9)$

(8, −4) →$(8\times1.5,-4\times1.5)=(12,-6)$

(4, −4)→$(4\times1.5,-4\times1.5)=(6,-6)$

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).