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)

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*1.5,6*1.5)=(12,9)`

(4, 6)→
`(4*1.5,6*1.5)=(6,9)`

(8, −4) →
`(8*1.5,-4*1.5)=(12,-6)`

(4, −4)→
`(4*1.5,-4*1.5)=(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).